AP Calculus AB

Power Rule

100

x^5

5x^4

200

3x^3

9x^2

300

47x^20

940x^19

400

12x^(-4)

-48x^(-5)

500

23πx^(-1/2)

((-23π)/2)x^(1/2)

P/Q Rule

100

(x)(3x) No simplifying!

3x + 3x

200

(5x)(sin(x))

5(sin(x)) + 5x(cos(x))

300

(3x^5)(tan(x))

15x^4(tan(x)) + 3x^5(sec^2(x))

400

(x^2)/(sin(x))

((2x)(sin(x)) - (x^2)(cos(x)))/ (sin(x))^2)

500

(5x^2)/cos(3x)

((10x)(cos(3x)) + 3sin(3x)(5x^2)) / ((cos(3x))^2)

Chain Rule

100

sin(2x)

2cos(2x)

200

((3 + x)^2)

2(3 + x)

300

((x^2 + 2)^3)

3((x^2 + 2)^2)(2x)

400

3(sin(x) + 4x^2)^(-4)

-12(sin(x) + 4x^2)^(-5))(cos(x) + 8x)

500

sin(cos(3x + 1))

-3(sin(3x + 1)(cos(cos(3x+1)))

Trig Rule

100

sin(x) ...if you don't get this...

cos(x)

200

tan(x)

sec^2(x)

300

csc(x)

-csc(x)cot(x)

400

arctan(x)

1/(x^2 + 1)^(1/2)

500

5arccos(x)

-5/(1 - x^2)^(1/2)

Log Rules

100

ln(x)

1/x

200

ln(5x)

1/x

300

log3(x)

1/(xln(3))

400

5log2(3x)

5/(xln(2))

500

ln(ln(x)

1/(xlnx)