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Mathematics /AP Calculus AB: Chapter 4 Practice Test

AP Calculus AB: Chapter 4 Practice Test

Mathematics20 CardsCreated 8 months ago

This set of flashcards covers the fundamental derivatives of simple functions including constants, polynomials, and root functions. It provides quick practice on applying basic differentiation rules such as the power rule and the derivative of constants and square roots.

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What is the derivative of the function f (x) = 5?

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Key Terms

Term

Definition

What is the derivative of the function f (x) = 5?

0

What is the derivative of the function f (x) = 2x?

2

What is the derivative of the function f(x)=−1/4x^6?

3/2x^7

Calculate f′(x) if f(x)=2x^9+8x^3+5.

18x ^8 + 24x ^2

What is the derivative of the function f(x)=−6x^2−3x^2−6x?

−12x+6/x^3−6

What is the derivative of the function f(x)=√x?

1/2√x

Compute the derivative of the function f (x) = (2x ^2 + 3) (4x − 6).

4x (4x − 6) + 4 (2x^ 2 + 3)

Compute the derivative of the function.

f(x)=(3x^2+1x)(2x^3−5x+7)

(6x−1/x^2)(2x^3−5x+7)+(3x^2+1x)(6x^2−5)

Compute the derivative of the function f(x) = (−3x^4+5x^2−√x+3)(x^−2−6x)

(-12x^3+10x−1/2x^−1/2)(x^−2−6x) +(-3x^4+5x^2−√x+3)(-2x^−3−6)

Compute the derivative of the function

f(x)=√x(4−x^2).

4−5x^2 / 2x^1/2

Compute the derivative of the function

f(x)=x−1/x+1.

2/(x+1)^2

Compute the derivative of the function

f(x)=1/x^2−x+2.

−2x+1 / (x^2−x+2)^2

Compute the derivative of the function

f(x)=√x−1/√x+1.

1/√x(√x+1)^2

Compute the derivative of the function f(x)=(x^2+x−3)^4

4(x^2+x−3)^3(2x+1)

Compute the derivative of the function f(x)=(5x^3−4x+1/x)^6

6(5x^3−4x+1/x)^5(15x^2−4−x^−2)

Compute the derivative of the function f(x) =

(x^2−3x+4 / 2x+3)10

(10(x^2−3x+4/2x+3)^9) (2x^2+6x−17/(2x+3)^2)

Compute the derivative of the function

f(x)=(x^2−1)^4 / x^2+1.

2x(x^2−1)^3(3x^2+5) / (x^2+1)^2

Compute the derivative of the function f(x)=1/√4x^2−5.

−4x / (4x^2−5)√4x^2−5

Compute the derivative of the function f(x)=(x+1/x)^3/5

3/5(x+x^−1)^−2/5(1−x^−2)

Compute the derivative of the function f(x)=(x^2−x)^3(3x+1) / x^4+2x^2−1.

(x^4+2x^2−1)[3(x^2−x)^2(2x−1)(3x+1) + 3(x^2−x)^3] −(x^2−x)^3(3x+1)(4x^3+4x) / (x^4+2x^2−1)^2

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AP Calculus AB: Chapter 4 Practice Test

Term	Definition
What is the derivative of the function f (x) = 5?	0
What is the derivative of the function f (x) = 2x?	2
What is the derivative of the function f(x)=−1/4x^6?	3/2x^7
Calculate f′(x) if f(x)=2x^9+8x^3+5.	18x ^8 + 24x ^2
What is the derivative of the function f(x)=−6x^2−3x^2−6x?	−12x+6/x^3−6
What is the derivative of the function f(x)=√x?	1/2√x
Compute the derivative of the function f (x) = (2x ^2 + 3) (4x − 6).	4x (4x − 6) + 4 (2x^ 2 + 3)
Compute the derivative of the function. f(x)=(3x^2+1x)(2x^3−5x+7)	(6x−1/x^2)(2x^3−5x+7)+(3x^2+1x)(6x^2−5)
Compute the derivative of the function f(x) = (−3x^4+5x^2−√x+3)(x^−2−6x)	(-12x^3+10x−1/2x^−1/2)(x^−2−6x) +(-3x^4+5x^2−√x+3)(-2x^−3−6)
Compute the derivative of the function f(x)=√x(4−x^2).	4−5x^2 / 2x^1/2
Compute the derivative of the function f(x)=x−1/x+1.	2/(x+1)^2
Compute the derivative of the function f(x)=1/x^2−x+2.	−2x+1 / (x^2−x+2)^2
Compute the derivative of the function f(x)=√x−1/√x+1.	1/√x(√x+1)^2
Compute the derivative of the function f(x)=(x^2+x−3)^4	4(x^2+x−3)^3(2x+1)
Compute the derivative of the function f(x)=(5x^3−4x+1/x)^6	6(5x^3−4x+1/x)^5(15x^2−4−x^−2)
Compute the derivative of the function f(x) = (x^2−3x+4 / 2x+3)10	(10(x^2−3x+4/2x+3)^9) (2x^2+6x−17/(2x+3)^2)
Compute the derivative of the function f(x)=(x^2−1)^4 / x^2+1.	2x(x^2−1)^3(3x^2+5) / (x^2+1)^2
Compute the derivative of the function f(x)=1/√4x^2−5.	−4x / (4x^2−5)√4x^2−5
Compute the derivative of the function f(x)=(x+1/x)^3/5	3/5(x+x^−1)^−2/5(1−x^−2)
Compute the derivative of the function f(x)=(x^2−x)^3(3x+1) / x^4+2x^2−1.	(x^4+2x^2−1)[3(x^2−x)^2(2x−1)(3x+1) + 3(x^2−x)^3] −(x^2−x)^3(3x+1)(4x^3+4x) / (x^4+2x^2−1)^2