For the function f (x) = 3*, estimate f'(1). From the graph of f(x), would you expect your estimate to be greater than or less than the true value of f'(1)?

Q: Find the anti-derivative of f'(x)=7x

A: Given : f'x = 7x

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: Find the derivative of the function.

A: Given: To find: Derivative

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

A: Given that,             f(x) = lnx3 Differentiating with respect to x, we get                  f'(x)…

Q: What is the derivative of the function f(x) = 2x + 3 at the number x = 4?

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

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Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

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Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

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Q: By using the First Principle, find the derivative of the following function at x = 2. 4x + 3 f(x) =…

A: We have to find the derivative of f(x)=4x+3x+1 at x=2 by using the First Principle.

Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: Find the derivative of the function. 8x f(x) = In f (x) =

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

A: Let us consider the given function as: fx=2xlnx By using product Rule of derivative, we get:…

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: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

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Q: What is the first derivative of p(x)=3^(x^5)?

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Q: If f(x) = 24x + 2, use the limit definition of the derivative to find the instantaneous rate of…

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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: Find the derivative of the function. f(x) = V5x + 4 f'(x) =

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Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=2 and f'(0)=3, what…

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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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: Find the derivative of the function. f(x) = (x + 1)(2x - 3) divided by 2x +1

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Q: Use the fact that the derivative of the function ​f(x)=4/x is f"(x)=-4/x2 to find the equation of…

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Q: Use the formal definition to find the derivative of f(x) = 4 at x = 8. x+3

A: To find the derivative of the function  f(x)=4x+3 at x=8

Q: Given the derivative f'(x), find the x-value for all relative extreme for the graph of the original…

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Q: Find the derivative with respect to x of f(x) = V5x + 4. f'(x) =

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Q: Find the derivative (x) = 2 In x – Vĩ

A: Given: fx=2lnx-x   As we know that; The sum/difference rule:  f±g'=f'±g' The Power law; ddxxn=nxn-1…

Q: What is the first derivative of f(x) = √√x² + 2x − 1?

A: Given the function,    fx=x2+2x-1

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 below: 4 f(x) + 1600 In(3 x7 x8 f'(x)

A: Given : fx = -4x7-5x8-6x9 + 1600ln3

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

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Q: Use the General Power Rule to find the derivative of the function. g(x) = V7- Sx

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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: Use the definition of derivative to find = f'(x). f(x) = for 1 3x

A: Given f(x)=13xf'(x)=limh→0f(x+h)-f(x)h=limh→0(13(x+h))-13xh=limh→013x+3h-13xh

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

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: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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

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

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Q: Find the derivative of f(x)= 11x^2 at x=1

A: Given:    f(x) = 11 x2  at x = 1

Q: Find the first derivative given that f(x) 5x V2r+3

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Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

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Q: Find the local extremes of f (x) = x³ +2x+ using the first derivative test.

A: Given,         The local extremes of fx=x3+34x4 using the first derivative test.

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

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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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Q: Use the definition of a derivative to find f'(x) for f(x) = v2x

A: Solution:Given     f(x)=2xTo find f'(x)Formula:By the defition of derivativef'(x)=limh→0f(x+h)-f(x)h