Differentiate the following using the Chain Rule: 2. H( X)= ( 2X+4)³ 3. h(x)= (3x-4)? 4. x (x)= 2 sin x 5. h ( x)= ( sin x)?

Q: Moreover, suppose F(x) = f(g(x)) and G(x) = g(f(x)). Use the chain rule to calculate the following…

A: f(x)=cot x  and  g(x)=5x-2

Q: Find the derivative of the following. Part 1: 95x+2 1. у 3D 3x2 +5 2. f(t) = 4tan 3t² cos 3t2 3.…

A: Given that some function and we find derivative of this function. We know that d(xn) /dx = nxn-1.…

Q: 1. Find the derivative of each of the following functions using chain rule: y=3x* (x* -2) a)

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Q: find (y') by Implicit differentiation e(2x+3y) = x² – In(xy³) 1 Add file

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Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: y=57x3+1-3

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -

A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)

Q: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

Q: Find the derivative of the following using First Principle. 4) y = -2x2 + 3x – 12 5) f(x) = x2 + 15x…

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Q: use the Chain Rule to find the derivative. y = cos3(e4θ )

A: Given: The function given is  y=cos3(e4θ)   To determine: The derivative of the function y=cos3(e4θ)…

Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

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Q: use the Chain Rule to find the derivative. y = cos3(12θ)

A: Here given as y=cos312θ

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: We have to find the derivatives of the following function: y=sin 4x3+3x+1 We know the formula of…

Q: what is the derivative of y=e^-1/2x(C1cos3x+C2sin3x) and evaluate if x=0, y'=8

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Q: Find the derivative of fG Cos' (3x²) 2. %3D

A: Consider the given function:…

Q: Find the second order derivative of ycos³(2x).

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Q: Find the derivative of the given function from the first principle ax2+bx+c

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Q: Find the second derivatives:y^n for y=1/8x^4-1/3x^3+3/4x^2-3x+5 And f(x)=2x/5x-2

A: (i): Given : y=18x4-13x3+34x2-3x+5 f(x)=2x5x-2…

Q: Find derivatives of the functions defined as follows: y =(3x3 - 4x)e-5x

A: Given:          y=3x3-4xe-5x Let:  y=f(x)=3x3-4xe-5x Product rule of differentiation is given by…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function is y=sin4 cosz. To find the derivative of the given functions. Solution: Chain rule…

Q: Use the Chain Rule to find the derivative. y = cos3(e4θ )

A: We have given y=cos3e4θ Then, dydθ=dcos3e4θdθ=3cos2e4θ-sine4θ4e4θ=-12e4θsine4θcos2e4θ

Q: Find the derivatives of the following functions using CHAIN RULE. y=(5x + 1)2

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=(sin(2x)+1)7f'π2=?f'(π)=?(a)  f'(x)=?(b)  which is bigger in between f'(π2) and f'(π)

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

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Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given- y=cos5t To use-  The Chain Rule to calculate the derivatives of the above function. Identity…

Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: Use the Chain Rule to find the derivative. y = cos3(12θ)

A: Given function is y=cos312θ. To find the derivative of the given function using chain rule.…

Q: 2. g'(x) where g(x)=x² +7x-5 %3D

A: In this question we need to find a derivative of the given function.

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function y=cos4θ+sin4θ The version 2 of the chain rule is  dydx=ddxfgx       =f'gx·g'x Here…

Q: f. y=In(x8+1)

A: We will solve the problem

Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: Find y" by implicit differentiation x2 5y2 5 + = 2 X у"-

A: Take d/dx on both sides and distribute it on the left side. Derivative of constant =0

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: 2. S- x²+1 dx x3+3x

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Q: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

Q: у %3D V1+ 2х (1 — х)-3

A:

Q: Find the second derivative of y = Vx² +x-3 O 6/x O 12/x^5 O 6/x^2 O 12/x^3

A: dxndx =n.xn-1 dcdx =0 ; where, 'c' is an constant number.

Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: у 3 cos (4x — 19)

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Q: Find the indicated derivative. dt for y(2.4t-3t)(2t+1.1)

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Q: Find the general solution of the following equation.Primes denote derivatives with respect to x.…

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Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

Q: Find y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x   and  y = (e-x)/…

A: Solution -a.)Given function -y = 5x2+6x-7lnxDifferentiating on both sides with respext to x,dydx =…

Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

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Q: 3r %3D 5r + 2 – 1 (d) f(x) =

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Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

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Q: y = (4x + 3)/ln[2x2 + 3x - 5] y = 3( e2x + e-2x )(x2 - 4

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Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

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