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Mathematics /AP Calculus AB: Chapter 5 Practice Test

AP Calculus AB: Chapter 5 Practice Test

Mathematics20 CardsCreated 7 months ago

This flashcard set covers key concepts in trigonometry and calculus, including finding cosine values from sine, and computing derivatives of trigonometric functions combined with polynomial expressions. It reinforces derivative rules for products and chain rule applications in trigonometric contexts.

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If sin x = 1/3, what is cos x ?

2√2/3

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Key Terms

Term

Definition

If sin x = 1/3, what is cos x ?

2√2/3

What is the derivative of f (x) = x sin x ?

sin x + x cos x

Compute the derivative of the function f(x)=cot(2x−1)?

-2csc^2(2x-1)

Compute the derivative of the function f(x)=tan(2x+1).

2sec^2(2x + 1)

What is the derivative of the function

f(x)=sin^3x+sec^3x?

3sin^2xcosx+3sec^3xtanx

What is the derivative of the function

f(x)=xsinx+1/cosx?

sinxcosx+x+sinx/cos^2x

What is the derivative of f(x)=e^2x

2e^2x

What is the derivative of y=xe^x+x^2 ?

e^x + xe^x + 2x

What is the derivative of f(x)=e^x+e−x/2?

e^x−e^−x/2

What is the derivative of the function f(x)=e^x−1/x^2+1?

x^2ex−2xex+ex+2x/(x^2+1)^2

What is the derivative of the function f(x)=e^xsinx?

e^xcosx+e^xsinx

What is the derivative of the function f(x) =e^x+1−1?

e^x+1

What is the derivative of the function

f(x) =x sinx/e^x−1?

(sinx+xcosx)(e^x−1)−xe^x sinx/(e^x−1)^2

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

1 / x

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

2^x ln 2

What is the derivative of y = x ln x − x ?

ln x

What is the derivative of the function

f (x) = sin x (e^x ) − cos x (e ^2x )?

e^x cos x + e^x sin x + e^2x sin x − 2e^2x cos x

What is the derivative of the function

f (x) = x^x?

x^x(lnx+1)

What is the derivative of the function f(x)=√ln2x?

1/2x√ln2x

What is the derivative of the function

f (x) = ln (x + ln x)?

1/x+lnx (1+1x)

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AP Calculus AB: Chapter 5 Practice Test

Term	Definition
If sin x = 1/3, what is cos x ?	2√2/3
What is the derivative of f (x) = x sin x ?	sin x + x cos x
Compute the derivative of the function f(x)=cot(2x−1)?	-2csc^2(2x-1)
Compute the derivative of the function f(x)=tan(2x+1).	2sec^2(2x + 1)
What is the derivative of the function f(x)=sin^3x+sec^3x?	3sin^2xcosx+3sec^3xtanx
What is the derivative of the function f(x)=xsinx+1/cosx?	sinxcosx+x+sinx/cos^2x
What is the derivative of f(x)=e^2x	2e^2x
What is the derivative of y=xe^x+x^2 ?	e^x + xe^x + 2x
What is the derivative of f(x)=e^x+e−x/2?	e^x−e^−x/2
What is the derivative of the function f(x)=e^x−1/x^2+1?	x^2ex−2xex+ex+2x/(x^2+1)^2
What is the derivative of the function f(x)=e^xsinx?	e^xcosx+e^xsinx
What is the derivative of the function f(x) =e^x+1−1?	e^x+1
What is the derivative of the function f(x) =x sinx/e^x−1?	(sinx+xcosx)(e^x−1)−xe^x sinx/(e^x−1)^2
What is the derivative of f (x) = ln 2x ?	1 / x
What is the derivative of f (x) = 2^x?	2^x ln 2
What is the derivative of y = x ln x − x ?	ln x
What is the derivative of the function f (x) = sin x (e^x ) − cos x (e ^2x )?	e^x cos x + e^x sin x + e^2x sin x − 2e^2x cos x
What is the derivative of the function f (x) = x^x?	x^x(lnx+1)
What is the derivative of the function f(x)=√ln2x?	1/2x√ln2x
What is the derivative of the function f (x) = ln (x + ln x)?	1/x+lnx (1+1x)