- Derivatives >. The derivative of the fourth derivative f (4) (x) is called the fifth derivative. It is denoted as f (5) (x).. This is an uncommon derivative, but it's sometimes used in physics where it's defined as the fifth derivative of the position function with respect to time.. Fifth Derivative Exampl
- Position and its various derivatives define an ordered hierarchy of meaningful concepts. There are special names for the derivatives of position (first derivative is called velocity, second derivative is called acceleration, etc.), up to the eighth derivative and down to the -5th derivative (fifth integral)
- Position or displacement and its various derivatives define an ordered hierarchy of meaningful concepts. There are special names for the derivatives of position (first derivative is called velocity, second derivative is called acceleration, and some other derivatives with proper name), up to the tenth (10th) derivative and down to the -11th derivative or eleventh integral
- The fourth, fifth, and sixth derivatives of position are known as snap (or, perhaps more commonly, jounce), crackle, and pop.The latter two of these are probably infrequently used even in a serious mathematics or physics environment, and clearly get their names as humorous allusions to the characters on the Rice Krispies cereal box
- 5th derivative of position Snap, Crackle and Pop - Wikipedi . Snap, crackle and pop are terms, based on the Rice Krispies mascots, used for the fourth, fifth and sixth time derivatives of position. The first derivative of position with respect to time is velocity, the second is acceleration, and the third is jerk ; g) the higher order derivatives
- g a is not constant, this function could be very important. In addition, the third derivative of position is also the second derivative of velocity, which means that it could still be to garner information about velocity as well (e.g., concavity, etc.)
- Larry, Moe, and Curly are 7, 8, and 9. When asked its name, the tenth derivative simply said a tenth derivative has no name. and returned to its service of the many-faced god. Okay, I lied They don't have names. We have a perfectly good way of.

What practical roles do the 4th, 5th, 6th, 7th, and 8th derivative of displacement have? (snap, crackle, pop, lock, and drop) quickly push the pedal to a position X and let your car accelerate from there, or B) gradually push the pedal to position X so your car has more acceleration near point X than near point 0, or C). The Derivative Calculator supports computing first, second, , fifth derivatives as well as differentiating functions with many variables (partial derivatives), implicit differentiation and calculating roots/zeros. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions

- Because we don't care. In decreasing significance, we care about: 1. Where things are* - normally very important. The elephant is in the room. 2. How fast they are moving - usually quite important. Can actually be more important that where you are..
- Applications of higher-order derivatives of position One of the first things we learn in physics is that velocity is the rate of change of position, acceleration is the rate of change of velocity, and how to figure out the quantities you don't know based on the ones you do
- It is well known that the first derivative of position (symbol x) with respect to time is velocity (symbol v) and the second is acceleration (symbol a). It is a little less well known that the third derivative, i.e. the rate of change of acceleration, is technically known as jerk (symbol j )
- 0th derivative: position. 1th derivative: velocity. 2th derivative: acceleration. 3th derivative: jerk = jounce = surge = lurch (some applications listed at Wikipedia) 4th derivative: jive = jounce = snap. 5th derivative: crackle. 6th derivative: pop. edit: Got some! The beam equation apparently uses fourth orders. The beam equation contains a.
- I've read something on this years ago which stated the fourth derivative of position is position again and I never could understand it. It was also discussed in The Reflexive Universe (1978) by Arthur M Young (1905-1995), a mathematician and aeronautical engineer of specializing in helicopters
- A useful thing to do with position data (e.g. from a motion capture system) is to calculate the first and second derivatives, which will give you the velocity and acceleration respectively. But it is possible to continue calculating derivatives. Here are the names for the first 10 ones: original: position velocity (1st) acceleration (2nd) jer

Mathematically jerk is the third derivative of our position with respect to time and snap is the fourth derivative of our position with respect to time. Acceleration without jerk is just a consequence of static load. Jerk is felt as the change in force; jerk can be felt as an increasing or decreasing force on the body ** History**. The elf-like characters were originally designed by illustrator Vernon Grant in the early 1930s. The names are an onomatopoeia and were derived from a Rice Krispies radio ad: . Listen to the fairy song of health, the merry chorus sung by Kellogg's Rice Krispies as they merrily snap, crackle and pop in a bowl of milk 9th derivative of position. Sep 26, 2020. 2) Water/Liquid played instruments. Placement. Modern primed notation: Derivatives are marked as primed functions, e.g.. Modern sublabel notation: Derivatives are marked with a subindex label denoting the variable with respect to we are making the derivative

- The 1st Derivative is the velocity The 2nd Derivative is the acceleration The It is well known that the first derivative of position (symbol x) with respect to (symbol s), crackle (symbol c) and pop (symbol p) for the 4th, 5th and 6th derivatives respectively. Higher derivatives do not yet have names because they do.
- 2) Now the plane starts moving, you are not still anymore, and the first derivative of the position function is positive. 3) Not only are you moving, but the plane brutally accelerates. As a result of the acceleration, you feel like someone is pushing you toward the back of your seat: the second derivative of the position function is positive
- <p>. </p> <p>Preshot. </p> <p>The dimensions of snap are distance per fourth power of time. Dimensions: . These instruments produce sonic waves playing the flux of plasma (Fire). Momentum equals mass times velocity. </p> <p>In Physics, displacement or position is the vector that specifies the change in position of a point, particle, or object. Likewise, presement, presity, preseleration.

- The fourth derivative of an object's displacement (the rate of change of jerk) is known as snap (also known as jounce), the fifth derivative (the rate of change of snap) is crackle, and - you've guessed it - the sixth derivative of displacement is pop. As far as I can tell, none of these are commonly used
- This explains where the higher order derivatives of acceleration can be used and how they can be understood
- Derivative A financial contract whose value is based on, or derived from, a traditional security (such as a stock or bond), an asset (such as a commodity), or a market index. Derivative Security Futures, forwards, options, and other securities except for regular stocks and bonds. The value of nearly all derivatives are based on an underlying asset.
- It is well known that the first derivative of position (symbol x) with respect to time is velocity (symbol v) and the second is acceleration (symbol a). It is a little less well known that the third derivative, i.e. the rate of increase of acceleration, is technically known as jerk (symbol j )
- There is no universally accepted name for the fourth derivative, i.e. the rate of change of jerk, but the term jounce is said to have been used. Another less serious suggestion is snap, crackle and pop for the 4th, 5th and 6th derivatives respectively

** In the preceding example, diff(f) takes the derivative of f with respect to t because the letter t is closer to x in the alphabet than the letter s is**. To determine the default variable that MATLAB differentiates with respect to, use symvar: symvar(f, 1) ans = t. Calculate the second derivative of f with respect to t The fourth and higher time derivatives of position are not used often enough for there to be a serious established word for them. Snap has been proposed for the fourth derivative, naturally followed by crackle and pop for the fifth and sixth derivatives The entire wiki with photo and video galleries for each articl Velocity is the derivative of position, so in order to obtain an equation for position, we must integrate the given equation for velocity: The next step is to solve for C by applying the given initial condition, s(0)=5: So our final equation for position is

In physics, derivatives of acceleration are very rarely used, and if used, rarely with their names. In any case, acceleration can be an arbitrary function, thus having arbitrary derivatives. In the case of your car, jerk isn't going to be a constant; rather, it's going to be zero, with slight changes needed to adjust the acceleration, which itself is needed to adjust the velocity A third derivative tells you how fast the second derivative is changing, which tells you how fast the rate of change of the slope is changing. If you're getting a bit lost here, don't worry about it. It gets increasingly difficult to get a handle on what higher derivatives tell you as you go past the second derivative,. If p(t) gives the position of a planet as a function of time, find the planet's velocity when t=0. Velocity is the first derivative of position. Therefore, all we need to do to solve this problem is to find the first derivative of p(t) and then plug in 0 for t and solve The model is very simple, having only 2 variables and 2 equations. The position of the particle is set by a function, and a velocity is calculated outside in the model. To get the velocity, however, Dymola must take a derivative of the ParticlePosition function, and it is in taking that derivative that Dymola trips ** Find the derivatives of various functions using different methods and rules in calculus**. Several Examples with detailed solutions are presented. More exercises with answers are at the end of this page. Example 1: Find the derivative of function f given by Solution to Example 1

- Take Derivatives of a Signal. Open Live Script. You want to differentiate a signal without increasing the noise power. MATLAB®'s function diff amplifies the noise, and the resulting inaccuracy worsens for higher derivatives. To fix this problem, use a differentiator filter instead
- The Derivative of a Single Variable Functions. This would be something covered in your Calc 1 class or online course, involving only functions that deal with single variables, for example, f(x).The goal is to go through some basic differentiation rules, go through them by hand, and then in Python
- Higher derivatives of displacement are rarely necessary, and hence lack agreed-on names. The fourth derivative of position was considered in development of the Hubble Space Telescope's pointing control system, and called jounce
- Whenever we speak of rates of change, we are really referring to what mathematicians call derivatives. Thus, when we say that velocity (v) is a measure of how fast the object's position (x) is changing over time, what we are really saying is that velocity is the time-derivative of position
- Because the derivative of a function y = f( x) is itself a function y′ = f′( x), you can take the derivative of f′( x), which is generally referred to as the second derivative of f(x) and written f( x) or f 2 ( x).This differentiation process can be continued to find the third, fourth, and successive derivatives of f( x), which are called higher order derivatives of f( x)

For example, the derivative of the distance (output value or the y-axis) of a moving object with respect to time ( input value or the x-axis) is the object's velocity ( v = d/t ): this measures how quickly the position of the object changes when time advances Defining the derivative of a function and using derivative notation Math · AP®︎/College Calculus AB · Differentiation: definition and basic derivative rules · Defining average and instantaneous rates of change at a poin Parametric Derivative Formulas. Parametric Equations. Parametric Integral Formula. Parametrize. Parent Functions. Parentheses. Partial Derivative. Partial Differential Equation. Partial Fractions. Partial Sum of a Series. Partition of an Interval. Partition of a Positive Integer. Partition of a Set. Pascal's Triangle. Pentagon. Per Annum. Peter's and Mike's answers have clearly settled this question; I'll just explain the OP's mention of Mathematica says that it is some hypergeometric distribution.More specifically, one wonders how Mathematica might have arrived at the Kummer confluent hypergeometric function ${}_1 F_1\left({{a}\atop{b}}\mid x\right)$.. We start with the transformed Maclaurin series Derivatives give slope, or rate of change with time. Acceleration (3rd derivative of displacement) gives rate of change of velocity, but if velocity is not changing at a constant rate, we apply 4th derivative. If acceleration is not changing at a constant rate, we apply 5th, and so on

** has a continuous first derivative**. Sometimes a continuous second derivative is also FIG U RE 7.1: In executing a trajectory, a manipulator moves from its initial position to a desired goal position in a smooth manner Crackle is the facetious name of a high-order derivative, and more specifically, the fifth derivative of the displacement. There is little consensus on what to call derivatives past the 4th derivative, jounce, due to there being few well-defined practical applications. The terms are, however, utilized within the fields of robotics and human motion

- This derivative curve is usually referred to as the hodograph of the original Bézier curve. Note that P i+1 - P i is the direction vector from P i to P i+1 and n (P i+1 - P i) is n times longer than the direction vector. Once the control points are known, the control points of its derivative curve can be obtained immediately
- The original formulation is F = dp/dt, but if mass is constant you can take it outside the derivative. If not, then you will need to account for the momentum carried into or out of the system by the mass (change). May 5, 2011 #5 DrBloke. 19 0
- If you take another
**derivative**on ③ (therefore total twice), you will get E(X²). If you take another (the third)**derivative**, you will get E(X³), and so on and so on. When I first saw the Moment Generating Function, I couldn't understand the role of t in the function, because t seemed like some arbitrary variable that I'm not interested in. . However, as you see, t is a helper var - The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. You can also get a better visual and understanding of the function by using our graphing tool

Commodity derivatives: Position reporting and position limits under MiFID II Posted on July 19, 2017 Commodity derivative trading is just one of the many topic areas under MiFID II that firms need to ensure they are prepared for before 3 January 2018 With the derivative method, the 1st-order derivative of B z (x) is obtained (Fig. 8(b)). A low-pass filter is used to filter noise signal. The 3rd-order and 5th-order derivatives of B z (x) are shown in Fig. 8(c and d) in the same way, respectively. Download : Download full-size image; Fig. 8 The sixth edition of the Balance of Payments and International Investment Position Manual (BPM6), updates the fifth edition that was released in 1993. The update was undertaken in close collaboration with the IMF Committee on Balance of Payments Statistics (Committee) and involved extensive consultations with national compilers, and regional and international agencies over many years the derivative. For example, if the position function s(t) is expressed in me-ters and the time t in seconds then the units of the velocity function ds dt are meters/sec. In general, the units of the derivative are the units of the dependent vari-able divided by the units of the independent variable

If L was the derivative of the real valued fn. we are thinking of, l is the gradient of the function. In our discussion, det(S) and (1/3)tr(s^3) are equal real-valued functions on the set of deviatoric symmetric tensors. Thus it only makes sense to ask that their derivatives, or their gradeints in the above sense, be equal in this space The derivative of jerk is sometimes called jounce (so it is the 4th derivative of position). Another suggestion is to refer to the 4th, 5th, and 6th derivatives of position as snap, crackle, and pop, respectively. Jerk and snap have many applications in engineering and science home / study / math / calculus / calculus solutions manuals / Bundle: Applied Calculus, 5th + Enhanced WebAssign - Start Smart Guide for Student + Enhanced WebAssign Homework Printed Access Card for One Term Math and Science / 5th edition / chapter 5.3 / problem 98

- Depending on what you mean by measure, you can also measure them. For example measure position, or one of its deriviatives, in the time domain and do a Fourier transform to calculate the others. Whether there is any practical use for the higher derivatives is a different question. $\endgroup$ - alephzero Apr 30 '17 at 23:4
- 5th derivative of position keyword after analyzing the system lists the list of keywords related and the list of websites with related content, in addition you can see which keywords most interested customers on the this websit
- Problem 2.4. Suppose that in September 2018 a company takes a long position in a contract on May 2019 crude oil futures. It closes out its position in March 2019. Options Futures and Other Derivatives John C. Hull - StuDocu John C. Hull is a Professor of Derivatives and Risk Management at the Rotman School of Management at the University of.
- In [14], derivative method is used to measure the position of branches of grounding grid. 1st, 3rd and 5th order derivatives of the surface magnetic ﬂux density are taken and the position of the pea
- Crackle is the facetious name of a high-order derivative, and more specifically, the fifth derivative of the displacement. [1] There is little consensus on what to call derivatives past the 4th derivative, jounce, due to there being few well-defined practical applications.The terms are, however, utilized within the fields of robotics and human motion

Options, Futures, and Other Derivatives 7th Edition. John C. position in an option pdf form of gathering blue or other derivative.J. Hull, Options, Futures and Other Derivatives, 7th Edition. john hull options futures and other derivatives 7th edition pdf Derivatives: A Student Introduction, Cambridge University Press, 1995 Finite Math and Applied Calculus (5th Edition) Edit edition. Problem 98E from Chapter 12.3: If we regard position, s, as a function of time, t, what is Get solution

* To achieve this, a method that uses both the back electromotive force (EMF) and the saliency to identify the flux position in the IPMSM without the injection of high-frequency components at low speeds has been reported*. We propose the extended method by controlling q-axis current derivative during zero voltage vector Frechet derivative is a generalization of the ordinary derivative and the first Frechet derivative is Linear operator. When you study differential calculus in Banach spaces you need to study.

Acceleration is the derivative of velocity with time, but velocity is itself the derivative of position with time. The derivative is a mathematical operation that can be applied multiple times to a pair of changing quantities. Doing it once gives you a first derivative. Doing it twice (the derivative of a derivative) gives you a second derivative For simplicity, we have assumed that derivative of function is also provided as input. Example: Input: A function of x (for example x 3 - x 2 + 2), derivative function of x (3x 2 - 2x for above example) and an initial guess x0 = -20 Output: The value of root is : -1.00 OR any other value close to root * There is one less long position and one less short position*. 7. Who initiates delivery in a corn futures contract A. The party with the long position B. The party with the short position C. Either party D. The exchange Answer: B The party with the short position initiates delivery by sending a Notice of Intention to Deliver to the exchange

According to MAR40.16 to MAR40.18, the offsetting treatment is applied to a cash position that is hedged by a credit derivative or a credit derivative that is hedged by another credit derivative, assuming there is an exact match in terms of the reference obligations * options futures and other derivatives solutions manual 5th pdf Interest rate derivatives, standard market models, 1-factor and 2-factor*. Receiving fixed in one security vs. A short position paying fixed in another, with. Model building and solution techniques. Options, Futures and Other Derivatives 7th Edition with Solution Manual

More formally, a function (f) is continuous if, for every point x = a:. The function is defined at a.In other words, point a is in the domain of f, ; The limit of the function exists at that point, and is equal as x approaches a from both sides, ; The limit of the function, as x approaches a, is the same as the function output (i.e. the y-value) at a.; Order of Continuity: C0, C1, C2 Function Preposition definition is - a function word that typically combines with a noun phrase to form a phrase which usually expresses a modification or predication. How to use preposition in a sentence. What is a preposition

- Get the free Partial derivative calculator widget for your website, blog, Wordpress, Blogger, or iGoogle. Textbook Authors: Stewart, James , ISBN-10: 1285741552, ISBN-13: 978-1-28574-155-0, Publisher: Cengage Learning. The third, the 4th, the 5th component is the partial derivative with respect to the 5th variable, very important
- ation of rotor.
- Quintic (5th order) — Requires 6 boundary conditions: position, velocity, and acceleration at both ends Similarly, higher-order trajectories can be used to match higher-order derivatives of.
- The big idea of differential calculus is the concept of the derivative, which essentially gives us the direction, or rate of change, of a function at any of its points. Learn all about derivatives and how to find them here
- Equation of motion, mathematical formula that describes the position, velocity, or acceleration of a body relative to a given frame of reference. Newton's second law, which states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration a of its centre of mass, F = ma, is the basic equation of motion in classical mechanics

Get help with your Differentiation of trigonometric functions homework. Access the answers to hundreds of Differentiation of trigonometric functions questions that are explained in a way that's. Play this game to review Pre-calculus. FInd the derivative: f(x) = (-2/3)x 3 - (1/2)x 2 + 9 On the basis of the adsorptive characteristics of the cobalt(II) complex with 2-(5′-bromo-2′-pyridylazo)diethylaminophenol at a hanging mercury drop

Derivatives of the 5th pharyngeal pouch It is a rudimentary structure and becomes part of the fourth pouch contributing to formation of thyroid C-cells. Derivatives of the 6th pharyngeal pouch The sixth pharyngeal pouch does not exist. The fourth and sixth arches contribute to the formation of the musculature and cartilage of the larynx Can anyoen help me with the following problem? A light shines from the top of a pole 50 ft. high as a ball is dropped from the same high from a point 30 ft. away from the light. How fast is the shadow moving along the ground .5 seconds later? (ball falling according to s = 16t^2

Detects peaks by looking for downward zero-crossings in the smoothed first derivative that exceed SlopeThreshold and peak amplitudes that exceed AmpThreshold, and returns a list (in matrix P) containing the peak number and the measured position and height of each peak (and for the variant findpeaksxw, the full width at half maximum, determined by calling the halfwidth.m function) The piston pin position is the position from crank center to the piston pin center and can be formu-lated from cosine rule of the trigonometry in fig.2 l2 r2 s2 2rscos( ) (16) From the above polynomial equation degree two we can drive the piston position as follows: s rcos( ) l2 r2 sin2 ( ) . (17) 2.1.5 Piston Pin Velocity The Applications of derivatives: Motion along a line exercise appears under the Differential calculus Math Mission. This exercise practices the position, velocity and acceleration of particles along a line. Types of Problems There are two types of problems in this exercise: Answer the problem about the particle: This problem provides the rule for a particle in motion. The user is expected to. My application is in using the first and second derivative of angular displacement data to yield velocity and acceleration. I have smoothed the displacement data, collected at 100Hz, with a forward and reverse 5th order butterworth filter (1/50 'low') prior to calculating velocity and acceleration

You have seen that the derivative of a function gives the rate of change of that function at the point of evaluation. Thus, if x (t) gives the position of the object at time t and the position function is differentiable, then the derivative x (t) gives the rate of x (t) gives the position of the object at time t and the position function is differentiable, the In continuation of research on C‐7 position of FQs, a novel series of 7‐[4‐(5‐amino‐1,3,4 thiadiazole‐2‐sulfonyl)]‐1‐piperazinyl fluoroquinolone derivatives 20a-20d have been synthesized, and nearly, all of the compounds exhibited moderate to good activity against some Gram‐(+) bacteria, that is, S. aureus, E. faecelis, Bacillus sp (MIC = 1-5 μg/mL) and showed poor.

Example Derivatives of e. Proportionality Constant. When we say that a relationship or phenomenon is exponential, we are implying that some quantity—electric current, profits, population—increases more rapidly as the quantity grows In physics, jounce or snap is the fourth derivative of the position vector with respect to time, with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively; hence, the jounce is the rate of change of the jerk with respect to time.Jounce is defined by any of the following equivalent expressions: The following equations are used for constant jounce

The First Circuit has taken the position that the AFC test is inapplicable when the works in question relate to unprotectable elements set forth in § 102(b). Their approach results in a much narrower definition of derivative work for software in comparison to other circuits Determine whether the positions of the particle are relative max or min. d) Whe is the particle 2 units to the right of where it started? ** Hint : Find s(0) and now consider two 2 units to the right as 2+ or 2-. Set the value equal to the position function and solve. This a problem of my practice test, I'm having a hard time with it

The position of a moving car at time t is given by f(t) = at2 + bt + c, t > 0, w JEE Main 2020 (Online) 6th September Morning Slot | Application of Derivatives | Mathematics | JEE Mai Now let's look at E mixolydian in the 5th position (lowest fret is 5) Now let's look at E mixolydian in the 9th position (lowest fret is 9) Finally, let's look at E mixolydian in the 10th position (lowest fret is 10) That covers the 5 basic positions and the open position of E mixolydian along the guitar fretboard

It is well known that the first derivative of position (symbol x) with respect to time is velocity (symbol v) and the second is acceleration (symbol a).It is a little less well known that the third derivative, i.e. the rate of change of acceleration, is technically known as jerk (symbol j).Jerk is a vector but may also be used loosely as a scalar quantity because there is not a separate term. The derivative technique can give you another layer of house meaning simply by looking at the 12-fold process of any of the ten planets. How? You simply start with the position of a single planet in the house it occupies and mentally recognize it as that planet's first house expression Voet, Voet and PrattsFundamentals of Biochemistry, 5th Editionaddresses the enormous advances in biochemistry, particularly in the areas of structural biology and Bioinformatics, by providing a solid biochemical foundation that is rooted in chemistry to prepare students for the scientific challenges of the future. While continuing in its tradition of presenting complete and balanced coverage. Linear motion (also called rectilinear motion) is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension.The linear motion can be of two types: uniform linear motion with constant velocity or zero acceleration; non uniform linear motion with variable velocity or non-zero acceleration

**Derivative** **of** a Constant Velocity. Let's say you're in your car, and you're going exactly 60 miles per hour. You know already that this is your rate of change, or how your **position** is changing as. In physics, jounce or snap is the fourth derivative of the position vector with respect to time, with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively; hence, the jounce is the rate of change of the jerk with respect to time. The notation is not to be confused with the displacement vector commonly denoted similarly You buy for a price and in the future you have a right of buy or not, depending of the price share, for instance. One of the parties is long position and the other party is short position. In this picture has a long call position. Source: Hull, C. John, Options, Futures and Other Derivatives, 5th Edition. Acknowledgements: Gustavo Carvalho Engineering Mechanics: Dynamics Effect of Altitude on Gravitation •Force of gravitational attraction of the earth on a body depends on the position of the body relative to the earth •Assuming the earth to be a perfect homogeneous sphere, a mass of 1 kg would be attracted to the earth by a force of: • 9.825 N if the mass is on the surface of the earth • 9.822 N if the mass is at an.

2.1 The Newton-Raphson Iteration Let x 0 be a good estimate of rand let r= x 0 + h.Sincethetruerootisr, and h= r−x 0,thenumberhmeasures how far the estimate x 0 is from the truth. Since his 'small,' we can use the linear (tangent line) approximation to conclude that 0=f(r)=f(x 0 + h) ˇf(x 0)+hf0(x 0); and therefore, unless f0(x 0)iscloseto0, hˇ− f(x 0) f0(x 0) It follows tha The derivative of sec(x) In calculus, the derivative of sec(x) is sec(x)tan(x). This means that at any value of x, the rate of change or slope of sec(x) is sec(x)tan(x). For more on this see Derivatives of trigonometric functions together with the derivatives of other trig functions The Commission on Oils, Fats, and Derivatives (1985—1990) [pages xv and xvij* Warning (revised) [page xvii]* pages where necessary so that new methods can be inserted in the correct position. Corrigenda/amendments It has been pointed out that certain corrections need to be made to the texts of some methods published in the 7th edition uses its dominant position in one relevant market to enter into, or protect, other relevant market. PREDATORY PRICE (under Section 4 Competition Act, 2002) The sale of goods or provision of services, at a price which is below the cost, as may be determined by regulations, of production of the goods or provision of services, with a view to reduce competition or eliminate the competitors Since mid-November, Binance Futures continued to dominate 75% of volumes on Binance its position as investors' appetite for derivatives trading grows. Chart 4 - Spot Bitcoin vs Bitcoin Futures weekly volume percentage. Source: Binance Futures, Data as of January 5th, 202