AP Calculus AB - Chapter 5 Review

Logarithms

100

dy/dx if y = ln|x+2|

What is 1/(x+2) ?

200

f'(x) if f(x) = ln|9x²-8|

What is (18x)/(9x²-8) ?

300

 f'(e) if f(x) = x²ln(x)

What is 3e ?

400

dy/dx if y = log₁₀(1+4x^-1)

What is -4x^-2/[ln(10)(1+4x^-1)] ?

500

y' for y = (ln(ln|x|))³

What is 3(ln(ln|x|))²/(xln|x|) ?

Exponentials

100

y' for e^4x+1

What is 4e^4x+1 ?

200

f'(-1) if f(x) = xe^x

What is 0?

300

f''(x) if f(x)=e^cos(x)

What is -cos(x)e^cos(x) + sin²(x)e^cos(x)?

400

dy/dx for y = 11^1-x

What is -11^1-xln(11)?

500

y' if y = sec(7^4x)

What is sec(7^4x)tan(7^4x)(7^4x)ln(7)*4 ?

Inverses

100

[f^-1(2)]' if f(x) = x³ + 2x - 1 and f(1)=2

What is 1/5 ?

200

f^-1(a) where f(x) = x³ - 4/x , a = 6, and f(2) = 6

What is 13 ?

300

dy/dx if y = arctan(x³-1)

What is 3x²/(1+(x³-1)²) ?

400

f'(x) if f(x) = sin^-1(2x)

What is 2/sqrt(1-4x²) ?

500

The derivative of f(x) = arctan(e^x)

What is e^x/(1+e^2x) ?

Integrals

100

The antiderivative of 7/x

What is 7ln|x| + C ?

200

The definite integral of f(x) = e^-x from x=0 to x=1

What is -e^-1 + 1?

300

The indefinite integral of 3x/(x²+1)

What is 3/2 * ln(x²+1) + C

400

The definite integral of 1/(xln(x)) on [e,e²]

What is ln(2) ?

500

The antiderivative of sec²(5x)*e^tan(5x)

What is (1/5)e^tan(5x)?

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100

The equation of the tangent line of f(x)=e^x-1 at x=2

What is y-(e²-1)=e²(x-2) ?

200

The open intervals where f(x)= x - e^x/3 is increasing

What is (-infinity,3.296) ?

300

Where f(x) = 3-ln|x| is concave up

What is (-infinity,0) and (0,infinity) ?

400

Find dy/dx for xe^y - 10x + 3y = 0

What is (10 + e^y)/(xe^y+3) ?

500

The average value of f(x) = 4^x-2 on the interval [3,5]

What is (1/2)*(60/ln(4)) = 30/ln(4) ?