Find an equation for f'(x), the inverse function. Verify that your equation is correct by showing that f(f¯'(x)) = x and f (f(x)) = x.

Q: Find the derivative of the function  y = ln (8x3-x2)

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Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

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

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Q: Find the second derivative of the function f(x) = 3*(square root of x+2 divided by 2x +1

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Q: Find the 3rd derivative of the function y=f(x) given by the equation y2=2x.

A: First we solve the given expression for y

Q: Find the derivative of the function f(x) = x√ln x

A: Here given Use the formula of product rule of derivatives as

Q: By using logarithmic differentiation and with respect to independent variable x, find the derivative…

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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 inverse function to f(x)=ex-e-x

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Q: Find the 100th derivative of  f(x) = xe−x.

A: f(x)=x.e-xwe can also write this asy=x.e-x      (EQUATION 1)differentiate both sides with respect to…

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

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Q: Find the derivative of the function x +5 g(x) = 2, X +6x

A: Given function is, g(x)=x2+5x2+6x  Quotient rule of derivatives is, If f(x) and k(x) are functions…

Q: Find the second derivative of the function. y = x sin2 x

A: Given information: The function is y==xsin2x To find the second derivative, first differentiable…

Q: (x) = ,2x+1

A: Explanation and solutions is given below....

Q: how do you find the second derivative of f(x)=ln(x)?

A: on differentiation we get

Q: x=1), 3. Y = In (x-1), (х-2)2

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Q: Find the derivative of f (x) = 1x , x = 0.

A: Given: f(x)=x at x=0

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Given, f(x)=9x3+1x On differentiating both sides w.r.t x we get:…

Q: FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 3. y = ln (x3(x-1)/(x-2)2)

A: using the properties of log lnmn=lnm-lnnlnmn=lnn+lnmlnmn=nlnm As per our guidelines we are supposed…

Q: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

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 second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: Find the second derivative of x² y² + xe = 2 sin y

A: Solution is given below:

Q: Find the second derivative of the function. In(x) f(x) 6x2 f"(x) =

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Q: Find the second derivative using implicit differentiation of x2+8y2=8

A: Given:

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

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

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Q: Find the second derivative of the function f(x) = sin (2x4)

A: This question is related to differentiation, We will solve it using given information.

Q: Find the derivative of the function. y = x2 In x2

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Q: Find the derivative of the inverse function  f(x) = x/x+2

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Q: Find the derivative of the function ° (2x + 1) f(x) = In x2 – 3 -

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Q: Find the second derivative of the function. f(x) = sin(9x?) f "(x)

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Q: Find the derivative of the inverse function at x=1 for the function y=sin(x−1)+x2.

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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 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 g(x) = ln √2x

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Q: Calculate the third derivative of the function y%-xe-",

A: To find the third order derivative we use product rule of derivative formula. From the product rule…

Q: Find the second derivative of 2x^2 ln (1/x^2)

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Q: Find the second derivative of the function. f(x) = x x sin(x) %3D f "(x) - !!

A: Given:   fx=x sinx  To find: f"x=?

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: Find the 1400th derivative of f(x) = xe-X.

A: Here we find derivatives of function.

Q: Find the derivative of f(x) = ln v4 – x2 %3D

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Q: Find the second derivative of the function f(x) = sec2x

A: Given: f(x)=sec2(x)

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: Find the derivative of the inverse function for y=x3−3x and calculate its value at x=−2.

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Q: Find the second derivative. f(x) = (5 + 4x)e−3x   f''(x) = ?

A: