AP Calculus AB: Chapter 5 Test
This flashcard set provides practice with computing derivatives involving trigonometric identities, products of functions, and composite functions using the chain rule. It also includes derivatives of exponential expressions and emphasizes combining multiple rules such as the product, quotient, and chain rules in one problem.
If sin x = 3/5, what is tan x ?
3/4
Key Terms
If sin x = 3/5, what is tan x ?
3/4
Find dy/dx of y=(3x^2−2)sin2x
6xsin^2x+2(3x^2−2)sinxcosx
Compute the derivative of the function f(x)=x^2−1/sinx?
2xcscx−(x^2−1)cotxcscx
Compute the derivative of the function f (x) = sec x.
tan x sec x
What is the derivative of the function f(x)=sin^2x+tan(x^2+1)?
2sinxcosx+2xsec^2(x^2+1)
What is the derivative of the function f(x)=sinx+1/sinx−1?
−2cosx/(sinx−1)^2
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| Term | Definition |
|---|---|
If sin x = 3/5, what is tan x ? | 3/4 |
Find dy/dx of y=(3x^2−2)sin2x | 6xsin^2x+2(3x^2−2)sinxcosx |
Compute the derivative of the function f(x)=x^2−1/sinx? | 2xcscx−(x^2−1)cotxcscx |
Compute the derivative of the function f (x) = sec x. | tan x sec x |
What is the derivative of the function f(x)=sin^2x+tan(x^2+1)? | 2sinxcosx+2xsec^2(x^2+1) |
What is the derivative of the function f(x)=sinx+1/sinx−1? | −2cosx/(sinx−1)^2 |
Find the derivative of f(x)=e^x^2. | 2xe^x^2 |
What is the derivative of f(x)=e^x−e^−x/2? | e^x+e^−x/2 |
What is the derivative of y=e^x−e^−x/e^x+e^−x? | 4/(e^x+e^−x)^2 |
What is the derivative of the function f(x) =e^x^2−1/1+sinx? | 2xe^x^2(1+sinx)-(e^x^2−1)cosx/(1+sinx)^2 |
What is the derivative of the function f(x)=e^sinx? | e^sinx*cosx |
| 3x^2+4e^2x |
What is the derivative of the function f(x) =sinx(1+e−x)/1+x? | (1+x)[(1+e^−x)cosx+(−e^−x)sinx]−(1+e^−x)sinx/(1+x)^2 |
What is the derivative of f(x)=ln1/x? | −1/x |
What is the derivative of f (x) = x ^2 ln x ? | 2x ln x + x |
What is the derivative of the function f(x)=lnx−1/lnx+1 | 2/x(lnx+1)^2 |
What is the derivative of the function f (x) = log _x 2? | −ln2/x(lnx)^2 |
What is the derivative of the function f(x)=ln(x+√x^2−1)? | 1/x+√x^2−1 * (1+x/√x^2−1) |
What is the derivative of the function f(x)=ln√x+1/x−1? | −1/(x+1)(x−1) |
What is the derivative of the function f(x)=lnx/lnx−1? | −1/x(lnx−1)^2 |