AP Calculus AB: Chapter 5 Practice Test
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.
If sin x = 1/3, what is cos x ?
2√2/3
Key Terms
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
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| 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) |
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) |