AP Calc AB Things to Memorize

d/dx of arcsin(x)

1/sqrt of (1-x²)

d/dx of arccos(x)

-1/sqrt of (1-x²)

d/dx of arctan(x)

1/1+x²

d/dx of arccot(x)

-1/1+x²

d/dx of arccsc(x)

1/(absolute value of x)(sqrt of x²-1)

d/dx of arcsec(x)

-1/(absolute value of x)(sqrt of x²-1)

integral of sinx

-cosx+C

integral of cosx

sinx+c

integral of a^x

a^x/ln(a) +C

integral of tan(x)

-ln|cos(x)|+C

integral of secx

ln|sec(x)+tan(x)|+C

integral of cscx

-ln|csc(x)+cot(x)|+C

integral of cotx

ln|sin(x)|+C

sin(2x)

2cos(x)sin(x)

cos(2x)

cos²(x)-sin²(x) or 1-2sin²(x) or 2cos²(x)-1

d/dx of a^x

a^x times ln(a)

d/dx of log to base a of x

1/(xln(a))

d/dx of sinx

cosx

d/dx of cosx

-sinx

d/dx of tanx

sec²(x)

d/dx of cot(x)

-csc²(x)

d/dx of cscx

-cscxcotx

d/dx of secx

secxtanx

sigma notation of i on bottom and n on top of i

n(n+1)/2

sigma notation of i on bottom and n on top of i²

n(n+1)(2n+1)/6

sigma notation of i on bottom and n on top of i³

n²(n+1)²/4

sigma notation of i on bottom and n on top of C

C*n

d/dx of a^f(x)

a^f(x)lna*f’(x)

integral of e^Cx

use u sub