Verify that the following function is a composite function f(x)=g(h(x)). f(x) = (In(x))-2 Identify the outside function g(h)= Identify the inside function h(x)- What simple rate of change rule can be used to find the derivative of the outside function? Find the derivative of f(x). Include proper notation in your answer.

Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x?

A:

Q: What is the derivative of f(x)=−3? Do not include "f′(x)=" in your answer. For example, if you found…

A: Formula:The derivative of a constant function is zero.

Q: Find the derivative of the function. 5 F(x) 1 + 4x + x3 F'(x) :

A:

Q: Find the derivative of: f(x) = (x3 + 2) In(x)

A: Consider the function

Q: Which function has the same derivative function f (x) as g(x) = lnx + x² – x?

A: we have to find derivative

Q: Find derivative of the function f(x)=x power3 -1/x-1

A: By applying the chain rule and quotient rule we find the derivative of a function.

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: derivative

A:

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Find the derivative of the function using the definition of derivative. 1 g(x) 8 + Vx g'(x) =

A:

Q: Find the derivative of the function. h(x)=7/x - 2/x^3 =1/x^4 h'(x)=

A: Given function h(x)=7x-2x3+1x4

Q: Find the derivative of the function: f(x)=e^-2x - e^2x

A: To find derivative of function.

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 derivative of the function g(x) = log3 √(1 − x)

A:

Q: Find the derivative of the function g(x) et 5x - g'(x) =

A: We have to use quotient rule for derivative and use  d/dx(ex)=ex d/fx(ax+b)=a

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: Find the derivative of the function. y In x2+9

A: Given function is: According to chain rule of derivatives:According to the quotient rule:

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.

A: Given function is hx=x+5x2+32 We have to find derivative of given function. To find derivative of…

Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

A:

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: f(x) = x In x

A:

Q: Find the derivative of the function: f(x)=ln x^2(x-3)^3÷(x+1)^4

A: To determine the derivative of given function.

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

A:

Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

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: Example 4:- By using the four steps rule, find the derivative of the function f(x) = Vx + 2

A:

Q: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

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

A:

Q: Find the 4th derivative of x^10 evaluated at x=0. What would be the 100th derivative of x^2000 be at…

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Q: Find the derivative of the function. f(x) = 4 3√x + 2cos x

A: The given function is ; f(x)=4/3sqrt(x) +2Cosx.

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 g(x) = ln(2x + 5)

A:

Q: o f(x) = 4~/x+3

A: by using definition of a derivative.

Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: 2х-3 3. у %3 Зx+4

A:

Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: Find the derivative of the function. g(x) = In(x – 5.1x=1) g'(x) =

A:

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

A:

Q: Find the derivative of f(x)=x^1/2 at x=1/144

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

A:

Q: Find the derivative of the function   f(x)=ln(x3(2x+1)/x^2−3)

A:

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

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Q: Suppose the first derivative of a function is f'(x) = (x- 30)(19x+ 1). The function f is decreasing…

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Q: Find the derivative of (x+5) / (x2-1) with respect to x.

A: Here we have to use formula of derivative  dxndx=nxn-1

Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

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

A: Differentiate w.r.t x

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

A: