2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second derivatives of f and g.

Q: Write the function as a composite f (g(x )) and compute the derivative using the Chain Rule.…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

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Q: 1. Explain how to use the differentiation part of the Fundamental Theorem of Calculus px 2+sin(4t)…

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Q: Use the Chain Rule to express the second derivative off o gin terms of the first and second…

A: Let y=f o g then we have to find the second derivative of y.

Q: Find the derivative of f(x) = In(x² + 1) %3D

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. x. 4 g(x)…

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

A: The chain rule of two functions fx and gx is given by the following formula. ddxfg(x)=f'g(x)·g'(x)…

Q: f(x) = cos (x – a -2).

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

A: Consider the function:  y=sin2x. Let u=2x  then  yu=sin u . Version two of chaon rule:…

Q: Find the derivatives of the functions in Exercise

A: Given: r=21θ+θ We know that ddxxn=nxn-1                                                        ..1

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

A: Consider the given function:…

Q: Find the derivative of the function. g(x) = In()x° – x|) %3D g'(x) = %3D

A: Formula used. ddxln(x)=1x;ddx(x)n=nxn-1

Q: Find the first three derivatives of y = x(In x)³

A: given problem :y=xlnx3

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

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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: Compute all second derivatives of f(1.y) = (x+) e- %3D

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Q: Compute the derivative of g(x) = cos(t) dt-

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Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

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Q: Determine whether the following statement is true or false, and explain why. The chain rule is used…

A: Given: The chain rule is used to take the derivative of a product of functions.

Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the func - 2t dt g(x) =…

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Q: Find the derivative of f(z) = 3+ 2x² – 2y² + i4xy .

A: We find out the derivative of given function .we differentiate both sides with respect to z and take…

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: Compute the derivative of f (x) = (x – 3r) cos(r). -

A: You will find the derivative of the given function using the product rule of differentiation which…

Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: Use the Chain Rule to express the second derivative of f ◦ g in terms of the first and second…

A: First, find the first derivative of the function, consider that the function f(x) and g(x) are…

Q: Find the derivative of f(x) = v3x + 1 using the general formula for differentiation.

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Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

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Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

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Q: 3. Calculate the derivative of f(x) = tan(4t) dt. %3D -1/16

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Q: g(=) = / Compute the derivative of g(x) dt. -2xe5 - 2xe - 2xe

A: Given           g(x) = ∫x21et3 dt

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: 3. Find the derivative of h()= 5²°-2z-1 %3D

A: We have to find derivative

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: Solution :1.fx=23x3-2xfirst derivative ,f'xf'x=29x2-2Second derivative…

Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

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Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

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

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = 3t…

A: By fundamental theorem of calculus, we have

Q: * Use the chain rule to find the derivative of

A: Given,        w = xy Here,         x=tan(t),   y=csc(t)

Q: Find the derivative of the given functions using chain rule. 1. f(x) = (2x + 1) 2. f(x) = (x² + 4x –…

A: To solve the following derivatives using chain rule and product as well as quotient rule.

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: In x g(x) = 2

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Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

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