Consider the function f(x) = . 125 If f-'(x) is the inverse function of f (x), find f-' (27).

Q: Find the derivative of f(x) = 2x/√x+1 if f'(2)

A: Given: fx=2xx+1 Formula Used: fg'=g.f'-f.g'g2

Q: Find the second derivative of the function. f(x) = 205√x

A: We use the power rule to find the first derivative

Q: Find the second derivative of the function. f(x) = 5x + 26x F"(x) =

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Q: Find the function whose derivative is 1-e2x

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Q: Find the derivative of the inverse function for y=2x3−1 and calculate its value at x=2.

A:

Q: Find the derivative and second derivative of g(x)=x(100-x^2)^(1/2).

A: Since the placement of the radical sign is not clear whether it includes x or no, the question has…

Q: Find the derivative of the function. f(x) = (9x2 – x) In(x) f'(x) =

A:

Q: Find the derivative of the function.

A: Use the chain and quotient rule of derivative to differentiate the function.

Q: Find the derivative of the function.

A: Given function is: f(x) = [ln (2x)]3 We have to find the derivative of the function.

Q: Find the second derivative of the function.         f(x) = csc x

A: Differentiating with respect to x, we get

Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 2n +4n in (2n) X

A: Follow the procedure given below.

Q: Find the third derivative if the function. 15. f(x)= 1/x

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Q: Find the derivative of the function. f(x) = 2- 5x-, - 6 f'(x) =

A:

Q: Find the derivative of f(x)= √8-x

A: We can solve using chain rule of derivative in order to solve the given problem.

Q: If the function f has a differentiable inverse function, the derivative of the inverse function f −…

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Q: use logarithmic differentiation to find the 1st derivative f(x)= x²(2x+3) (x²+1)*

A: given function  f(x)=x22x+3(x2+1)4

Q: find the derivative of the function F(x)=4(x^3-x)^4

A: According to the given information, it is required to find the derivative of the given function.

Q: Find the derivative of the function f(x) = 10 + x² + 14. x3 f'(x) =

A:

Q: Find the derivative of the function. f(x) = arcsec(4x) f'(x) = 1 x√ 16x² - 1

A:

Q: Find the derivative of the function.

A: Given: fx=ln 3x To Find: The derivative of the given function

Q: Find the derivative of the function. (x) - In(4 - x") f'(x) -

A: Find the derivative of the function.      fx=ln4-x8

Q: Find the second derivative of f(x) = x+2 X- 2

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Q: Find the derivative of the function by definition. 2- P0-x

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Q: find the derivative of the function f(x) = 7(x^3-x)^4

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Q: Use implicit differentiation to find the 2nd derivative of x2 y + y2 x=-2

A: By using implicit differentiation to find the 2nd derivative of x2y+y2x=-2.

Q: Find the derivative of the function g(x)=x3∫x2tdt.

A:

Q: Find the derivative of the function. f (x) = (4x - x 2 ) 100

A: Given, f(x)=(4x-x2)100

Q: Find the derivative of the algebraic function.

A: Differentiation is the process of finding the rate of change of one variable with respect to another…

Q: Differentiate f (x) = In(vx² + 1 sin* x) and write the derivative in its simplest form.

A:

Q: calculate the 21st derivative of function f(x) = 20-x

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Q: Find the 35th derivative of f(x)= sin.x.

A: Given,             fx=sinxTo find: The 35th derivative of fx=sinx.

Q: what is the derivative of 1/x2

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Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

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Q: Find the derivative of the function f(x)= x5 - 9/x4

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Q: Find the derivative of the ff. 3. f(x)= +an (x²- 2x) 8.h(x) = (4) -* -x2

A: Using chain rule.

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: Find the derivative of the function. f(x) = arcsec(4x) f (x)

A: Explanation of the answer is as follows

Q: Find the derivative of x²e*.

A:

Q: Evaluate the second derivative of the function below at (1, -2). y² = x³ = x + 1 -

A: To evaluate the second derivative of the function at the given point.

Q: Find the derivative of the function. f(x) = 4x In 4x f'(x)=

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Q: Find the derivative of the function f(x)=10/x^3

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Q: Find the thousandth derivative of f(x) = xe -x

A: Given function,  f(x) = xe-x  To find the thousandth derivative of f(x)

Q: Find the derivative of the function. 5/.3 x° +4x

A: Given that q=x3+4x5To find  the derivative q'

Q: What is the inverse process of determining a function whose derivative is known?

A: The inverse process of determining a function whose derivative is known is called

Q: Explain how to find the derivative of the function f(x) = cxn .

A: we have to explain how to find the derivative of the given function f(x)=cxn

Q: Find the second derivative of f(x)=x^3 + x-5

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Q: Find the equation of the tangent line to the inverse function of f = x +3x³+7x+2 at point (13, 1).

A: (13,1).

Q: Find value of derivative of the inverse of function. Given that f(x) = sin x + 4x, find (f^-1)'(0)

A: find explanation below

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

A: The function f(x)=lnx-3. We have to use the derivative to determine whether the function is strictly…

Q: What is the 1881th derivative of the function given by f(x)=1881x + 1923 at the point x=2020.

A: