For the following exercises, use the given values to find (f-')' (a).

Q: For the following exercise, use the definition of a derivative to find f'(x) f(x)=x+(1/x)

A: The definition of derivative is  f'(x)=limh→0f(x+h)-f(x)h

Q: Use the chain rule to find the derivative of  f(x)= 3(3x^10-6x^9)^17 You do not need to expand out…

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Q: f (x) e1/x x2

A: Given function is fx=e1xx2

Q: use the graph of y=f(x)y=f(x) to sketch the graph of its derivative f′(x).

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Q: For the following exercises, find the average rate of change of each function on the interval…

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Q: Use the Chain Rule to find the derivative.

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Q: Find f'(x) using derivative rules, f() = V + 2. メジ %3D

A: Given:…

Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (x) = 5x – 4

A: Note:- These are multiple questions and according to our company guideline we can do maximum 1…

Q: f(x) = Vx – 6

A: Given that                 f(x) =x-6      Differentiating with respect to x, we get           f'(x)…

Q: For the function f(x)=2x^3-12x^2+20, Use the SECOND DERIVATIVE TEST to find the relative extrema.

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Q: find the requested higher-order derivative for the given function... d2y/dx2 of y=3sinx +x2cosx

A: Given: y=3sinx+x2cosx The objective is to find the higher-order derivative d2ydx2 Let's find the…

Q: For the following exercises, use the definition of a derivative to find f′(x). 59.  f(x)= sqrt 2x

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Q: For the following exercises, use a graphing utility to estimate the local extrema of each function…

A: Given hx=x5+5x4+10x3+10x2-1

Q: For the following exercises, find the average rate of change of each function on the interval…

A: Consider the given function.

Q: 16) Find f'(x) using the definition of the derivative. f(x) = x3 + x

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Q: For the following exercises, use the definition of a derivative to find f′(x). 55.  f(x)=2−3x

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Q: For the function f(x) x + x3, find all of the relative and absolute extrema using the first or…

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Q: 2. g'(x) where g(x)= x² +7x-5 %3D

A: ddxxn = n·xn - 1, and ddxC =0

Q: Use the chain rule to find the derivative of f(x) = 2( – 72* – 8z*) 4 You do not need to expand out…

A: Given: f(x)= 2(-7x8-8x5)14

Q: Use the chain rule to find the derivative of 16 f(x) = 3( – 52° – 9x")" You do not need to expand…

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Q: Use the chain rule to find the derivative of 16 f(x) = 3(8r" - 5z ) * You do not need to expand out…

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Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: Calculate the following derivative if f(x) = x*. f(4)(2) = %3D

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Q: For the following exercises, find the average rate of change of each function on the interval…

A: Given y=1/x on [1,3] We need to calculate the average rate of change of y on given interval.

Q: For the following exercises, use the definition of a derivative to find f′(x). 58.  f(x)=5x−x^2

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Q: For the following exercises, determine whether the Mean Value Theorem applies for the functions over…

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Q: Given f(x) = Vx+ 8, find f' (-4) using the definition of a derivative. %3D Provide your answer…

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Q: Given f(x)=√x + 3, find f'(-2) using the definition of a derivative. Provide your answer below: ƒ'(…

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Q: f (x)=vx+2, a=6 it

A: Given function is  fx=x+27

Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: A1) Using the definition of derivative, find the derivative of f(z) = x + 5x + 5. %3D

A: Given f(x)=x^2+5x+5 Now we will find the derivative of given function using definition of derivative…

Q: Find the second derivative of the following function: f(x) = esin1, %3D

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Q: For the following exercises, find f '(x) for each function. Sa) = 10 In 10 1) 10 2) 10* 3) In 10 4)…

A: Find the derivative of the function

Q: 3. For the following exercises, use the graph of y= f(x) to sketch the graph of its derivative f'…

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Q: For the following exercises, state the domain and range of the function. 9. h(x) = ln(4x + 17) − 5

A: Given expression is : h(x) = ln(4x+17) - 5

Q: For the following exercise, find the average rate of change of each function on the interval…

A: We will find the average rate of change of given function as shown below

Q: Use the chain rule to find the derivative of 5(– 3a10 – 9a*)5 3x10 You do not need to expand out…

A: Given that: y=5(-3x10-9x4)15

Q: I need the third derivative for all of the following functions: f(x)= + 1 + x

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 12. Find f'(x) using the definition of the derivative.  f(x) = x3+ x

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Q: 2. For the following exercises, determine whether the Mean Value Theorem applies for the functions…

A: Mean value theorem states that 1. The function f(x) is continuous in the interval [a,b] 2. The…

Q: Use the chain rule to find the derivative of 3(– 82° – 2=")" - You do not need to expand out your…

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Q: For f(x) = 1/x-1  find the derivative and the domain of the derivative

A: Obtain the derivative of the given function as follows.

Q: Find f' (8) from f(x) = V7x – 2 using the definition of a derivative. (Do not include "f'(8) =" in…

A: This question is related to deivative.

Q: For the following exercises, find the average rate of change of each function on the interval…

A: Explanation of the solution is given below...

Q: For the following exercises, use the limit definition of derivative to show that the derivative does…

A: To find the derivative of a function by using the definition of a limit, fx=x2x2+1 at x=a, let f:…

Q: For the following exercises, find the differential of the function.   71.  y = x^2 + 2x − 1

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Q: For the following exercises, use the definition of a derivative to find f′(x). 54.  f(x)=6 55.…

A: Given: a) f(x)=6 b) f(x)=2-3x

Q: For the following exercises, use the definition of a derivative to find f′(x). 57) f(x)=4x^2 61)…

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Q: Use the second derivative   f''(x)=x(x−1)(x−3)^2 to determine where the inflection points of f(x)…

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