Find the derivative of the following function by first simplifying the exp x2 - 64 g(x) = x-8 .... g'(x) = everywhere that g(x) is differentiable.

Q: Use the General Power Rule where appropriate to find the derivative of the following functions.

A: We have to find the derivative of the function: y=lnx3+1π We know that lnam=m lna Therefore given…

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A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

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Q: Determine the derivative of the following function by applying the quotient rule.…

A: The given function is: h(x)=ln (x2+x)x2+1 The quotient rule for the derivative is given by:…

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

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Q: Find the derivative of the function. y = In(x8)

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Q: ; Compute the derivative of the function: f (x) = (+ Inx)² а.

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Q: calculate the derivative with respect to x. x3R5 = 1

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Q: Find the derivative of y with respect to x of y = xlnx – x.

A: Using rules of differentiation.

Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

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Q: Find the derivative of the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: 2. f(x) = x2– 5x + 6 at x 2 --

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Q: y = x*(1 – In x4)

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Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |

A: Given :            To find the derivative of the given function                f(x) = x3 -…

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: 2. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

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Q: Find the derivative of the following function. y= 4 ln x – In(x-8)

A: we have to derivative

Q: Find the derivative of the following function by definition (from first principle): f(x)= x/(x-1)

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Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Find the derivative of y = arctan² (x³)

A: This is a problem of differentiation of the function. Based on general formula we will solve this…

Q: 1. Y= 3x -x- 2

A: Find your answer below

Q: Find the derivative of the function h(x) = x2 arctan5x

A: The given function is h(x) = x2 arctan5x

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Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: Find the derivative of the function. f(x) = 18 In(x) %3D

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Q: find the derivative of y with respect to the givenindependent variable. y = log4 x + log4 x2

A: Given: By using logarithm base change rule, the function can be rewritten as follows,

Q: 19. Find the derivative of 16 = xy using implicit differentiation.

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Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

Q: Find the equation of the line tangent to the graph of the function f(x)=x-2x^2 at x=1 use the…

A: The equation of the curve is: f(x)=x-2x2

Q: Evaluate the derivative at the given value of x. 10) f(x) = x2 + 5x at x = 4 %3D

A: I did with limit definition of derivative

Q: Find the derivative of the following function by definition (from first principle): 1-x f(x) =. 2x

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Q: Find the derivative of the following functions using the long method (limits)

A: Given: x= 12 t4-5t-3 To Find: limh→0xt+h-xth

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Q: Find the derivative of f (x) =arcoth (e³" ).

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Q: Find the derivative of the following function by definition (from first principle): f(X)=1-x/2x

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Q: -5

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Q: Find the derivative of the following function, where x is already declared as a symbolic variable: f…

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Q: Find the derivative of the function. h(x) = ets. - x + 1

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Q: Find the derivative of the following function by definition (from first principle): f(x) = x-1

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Q: find the derivative of y with respect to the givenindependent variable. y = 3-x

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