Find the approximate value of derivative f'(0) with the step size h for the following function by using three point end point formula: f(x)=tan² ( 2 ), h= 3 O -2 O 2 10 3

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A: To find the nth derivative of function y.

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Q: Find the derivative dydx for the function x=sin2t, y=−cost at the point t=π6.

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Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

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A: We differentiate with respect to t using chain rule.

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

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Q: Find the derivative of the following functions using the long method (limits) (a) x =t-5t- 3 (b) y =…

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Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

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Q: 5. y= 2arctan(vx)

A: We need to evaluate the derivative of the following function y = 2arctanx

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: y=x4+cos(2x) Find derivative of given function with respect to x . Here use chain rule and then find…

Q: . Find the derivative with respect to x: y = tan¬(Vx² –- 1) + csc¯²(x),x > 1

A: Given thaty=arctanx2-1+arccscx To find its derivative

Q: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

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Q: find the derivative of y with respect to the appropriatevariable. = sin-1 (1 - t)

A: Given Trigonometric Expression: sin-11-t We can differentiate this trigonometric function with the…

Q: Find the derivative of the function

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Q: Find the second derivative for the functions defined as follows .p(x) = sin(x2)

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Q: Can you help me step by step?

A: Differentiate with respect to x,

Q: 2) Find the first derivative: a) y = cot * (3x² +7)

A: Differentiate wrt x

Q: Find the derivative of the function. 1 3x' g(x) = dt 1 + t4 Jtan x

A: Given : g(x) = ∫tanx3x211+t4dt

Q: find the derivative of y with respect to the appropriatevariable. y = sinh-1 √x

A: Find the derivative of y with respect to the appropriate variable.

Q: Find the derivative of the following function with respect to x x = sinh2y

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Q: Find the derivative with respect to x: y = tan(Vx2 – 1) + csc-(x),x > 1

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Q: find the derivative of y with respect to the givenindependent variable.

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Q: For a given equation, f(x) = xe* Compute the derivative at x = 2 using forward, backward and…

A: Given the function fx=xex.   The forward difference formula is given by f'a=fa+h-fah. The backward…

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

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Q: Find the derivative of the function g(x)= integral  x2  tanx  (1/square root 4+t4) dt

A: Leibnitz integral rule for Differentiation :               ddx ∫α(x)β(x) f(t,x) dt = ∫α(x)β(x)…

Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x =; using a…

A: The three-point midpoint rule to calculate f'(x) is f'(x)≈f(x+h)-f(x-h)2h, where h is the step size.

Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

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Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Given: y=xx+15 To Find: The derivative of the given function

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (t3/2) + √t

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Q: Compute the first-order Derivative for each of the following functions at the specified location and…

A: Since you have asked multiple questions, we  will solve the first question for you. If you want any…

Q: y = e* - cos 3x + xlog.(1+x)

A: By using some formula of derivative

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Q: Find the derivative of the function F(x) sin 3t cos 2t dt.

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Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

Q: Q2: What is the value of second derivative of f(x)=3 sin((1-x)/t) *

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Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

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Q: Q3: find the derivative of the following: 1. y = lnx + √1-x² sech-¹x 2. y= sinh-1(tanx)

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: The 2nd derivative of the function x = Ci cosot + C2 sin ot with respect to t is

A: Given function is

Q: find the derivative of y with respect to the appropriatevariable. y = sin-1√2 t

A: To find the derivative of y=sin-12t

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Q: Find the derivative of the function y, below. y = 2x(ln x + In 7) – 2x + V2 dy da

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Q: find the derivative of y with respect to the appropriatevariable. y = 1/2 sinh (2x + 1)

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: Use three-point midpoint formula to evaluate the first derivative of y = sin(x) at x = using a value…

A: To find- Use three-point midpoint formula to evaluate the first derivative of y = sinx at x = π2…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: