Calculus AB

Derivatives

100

Differentiate cotx

cotxsecx

200

Differentiate 6x+2

6

300

Differentiate (x²+1)³

6x(x²+1)²

400

Differentiate tanx

-sec²x

500

Differentiate -7/(2x-3)²

28/(2x-3)³

Integrals

100

Integrate 3xdx

3/2x²+3+C

200

Integrate 4x+1

2x²+x

300

Integrate 10^x

1/ln10(10^x)+c

400

Integrate x(x²+1)²dx

1/6(x²+1)³+C

500

Integrate sin²3xcos3xdx

1/9sin³3x+C

Logarithmic/Exponential

100

Find log₂1/8

-3

200

Differentiate 8^-x

-(ln8)(8^-x)

300

Differentiate y= 4(3^x)

4(ln3)(3^x)

400

Differentiate 5^{x^2+3}

(ln5)(5^{x^2+3})(2x)

500

Differentiate y=log₃cosx

-sinx/ln3(cosx)

Limits

100

What is the limit as x-->2 of (4x^2+3) ?

19

200

What is the limit as x-->0 of sinx²

0

300

What is the limit as x--> -3 of (x²+x-6)/(x+3)?

-5

400

What is the limit as x-->1 of (x³-1)/(x-1)?

3

500

What is the limit as x-->0 of sec2x?

1