Obtain the derivatives of the following functions f(æ), using the Simple chain rule and enter your answers as functions of x in the appropriate boxes. 1. f(x) = sin 8x, f'(x) = 2. f(æ) = sin( +8), f'(2) = | 3. f(x) = e*, f'(2) =|

Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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

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

A: Take 1+y = t  And use chain rule

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: Find for the following equation by Implicit Partial Differentiation; дz x³ + y²z4 + 3xyz = 5

A: Implicit partial differentiation

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: compute the derivatives indicated. f(x, y) = 3x²y – 6xyª, and ax2 ay2

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Q: Find the partial derivative of the given In[y? sec(x²y²)].

A:

Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

Q: Find Find the second derivative of the given function. y = In(x² – 1)

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Q: (a)Deduce the 1$, 20d and 3rd derivatives of y = cos²x.

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

Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: Use partial differentiation to find the derivative of the implicit function dy (3x'y-1)+ 7xy = 9…

A: We will use the given formula to solve this question.

Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

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

A: given problem :y=xlnx3

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: 12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y?…

A: We have to find derivative

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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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: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: 1. Find the first derivative of y: y=x-6x³+2x²

A: Topic = Derivative As per guidelines , At  a time only one question can be answered. please repost…

Q: Find the derivatives of the function defined as follows.

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Q: Find the derivatives of: d/dx (ex-e-x/ex-e-x) And the derivatives of: f(x)=ln((2x+1)3/(3x-1)4)

A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

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: find the first & second derivative of fox)=e 2. Cosx.

A: Given: The function fx=x2excosx, To find: First and second derivative of given function fx.

Q: Find the derivative of the function. y = (3x + 1)°(x+ - 6)° A y=(32x +9)(3x +1) (x*-6)° B y' = 9(3x…

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Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: Find the derivatives of the functions defined as . y = cos4 x

A: Given function, y = cos4 x

Q: 2. Find derivative of given function defined as follows 2x y = e = ²

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Q: Find Zxx=Zyy=Zxy=

A:

Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: Find the first derivative of g(x) if g(x) = e²* In(2x) %3D

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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: 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 derivative of f(x)=

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

Q: Find derivatives of the functions defined as follows: y = e-2x

A: The derivative of the function ex is ddxex=ex. Find the derivative of the function y=e-2x using…

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

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Q: Find derivatives of the functions defined as follows: y = e4x

A: The derivative of function to be found out is y=e4x

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

A:

Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

A:

Q: 2-х Find the derivative of y = Зx+1 -7 бх-5 6- А. (3х+1)2 В. (3x+1)2 7-6х С. (3x+1)2 D. (3x+1)2 Е.…

A: Proceed as shown below