3. (a) Differentiate the function f(x) = x2 from first principles.

Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

A:

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: Find the derivative of the algebraic function.

A:

Q: Find the derivative of a function f(x)=(x^2+1)^3 (2x−1)^4 f ' (1) = ____

A:

Q: 1. Find the derivative of f(x). 3x³ 2x²-x-5 - (a) f(x) = √x (b) f(x) =

A:

Q: Find the first and second derivatives of the functio f(x) = x(x² + 4)2 %3D f'(x) = %3D f" (x) = %3D

A:

Q: 1. Find the derivative of f(x) if f(x) = x7 + 10x5 – x² – 4

A:

Q: 2. Use the definition of derivative to find the derivative for f(x) = x2 + 3x . | f(x +h) – f(x) lim…

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Q: 1 Find the derivative of f(x) = 2x + 3

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Q: 5. Use the definition of derivatives to find f'(2) given that f(x) = 2x² -r+1

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: Find the derivative of the algebraic function.

A: we have to find the derivative of the function f(x)=x41-2x+1

Q: 16) Find f'(x) using the definition of the derivative. f(x) = x3 + x

A:

Q: Find the derivative of the function f(x) = 3x2- 13x 25 by definition of derivatives f(x + h) - f(x)…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find the derivative of the function. f(x) = In(x + V2 + x²) f '(x) =

A:

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

A:

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: Find the derivative of the function. f(x) = (x2 + 3) In(x) f'(x)

A:

Q: Find the derivatives of the function f(x) from the first principle x4+4

A: Here is the solution

Q: 2. Use the first and second derivatives to obtain sketches of the function below. 4x+2 f(x) = %3D…

A:

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: Find the anti-derivative F(x) of the function f(x) = 2x - 7 with F(2)=55- %3D

A: We have to find the anti derivative of the given function following the given condition. anti…

Q: 1. Find the second derivative of f(x) = x5 – 4x + 1. а. 5x3—4 ь. 20х3 с. -20х3— 4

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Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

A:

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: the derivative () of = f(x) = 2

A: Please refer to the image below

Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: (b) Find the derivative of f (x) = (x² + 2) (8x − 5) by using the product rule. Let g (x) = x² + 2…

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Q: 1 Find the derivative of f(x) 2x + 3

A: Since we have to find the derivative of f(x)=12x+33, so ddx(f(x))=ddx1(3+2x)3 -(i)By using the chain…

Q: 12. Find f'(x) using the definition of the derivative.  f(x) = x3+ x

A:

Q: 2. Find the derivative of f(x)= 2х — 3. Зх + 4

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: 1) Find the second derivative of f (x) = 24 . %3D

A:

Q: 1. Use the definition of derivative to find the derivative of (a) f(x) = (x + 1)² 1 (b) f(x) =…

A: The solution are next step

Q: Find the derivative of the algebraic function. f(x) = (4 − 3x − x2)/(x2 − 1)

A: We have to find the derivative of the algebraic function: fx=4-3x-x2x2-1 Rewriting the function,…

Q: 9. Use the definition of a derivative change of the functions below at f(x)% = x² + 2x

A:

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

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Q: 1) find the derivative of y = 4x2 – 3x – 2 | | then evaluate f'(x+3)

A:

Q: Find the derivative of the function f(x) = 8x² – 14x by the definition of derivatives f(x+h)-f(x)…

A: Given function: fx=8x2-14x

Q: Find the derivative of the algebraic function.

A: Given, fx=x1-4x+3

Q: 11. Use the definition of the derivative to find f'(x) for the function f(x) = x2 + x + 2. Show your…

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

Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

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

A:

Q: 2. Use the definition of the derivative to find f'(7) if f(x) = 4 + 3x – 2x.

A:

Q: 5. Find a function f(x) whose derivative is f'(x) = +1. (Hint: (x + 1)/x=1+1/x)

A: 5) derivative of a function is given, to find the function we have to find the anti derivative of…

Q: find the derivative of the function:   f(x) = det [ -1  -4  3  -4  -3 ]                  [  3   0…

A: To Determine: find the derivative of the function that is f'(x) Given we have a determinate…

Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

A:

Q: 7 Use the power rule to find the derivative of f(x) = x f'(x) =

A: Power Rule: The power for the derivative of the function xa is given by, The given function is f(x)…

Q: 3. If f(x) = 2x² + 3x find f'(a) by using definition of derivative at a point a=4

A:

Q: Apply your understanding of derivatives to determine any intervals of increase for the function…

A:

Q: What is the derivative of the attached function for x= -8   -1 -1/2 1 2

A: