Calc 2 - Derivative & Integral Rules (& Pythagorean identities!)

d/dx[e^x]

e^x

d/dx[a^x]

a^xlna

d/dx[lnx]

1/x

d/dx[log_ax]

1/xlna

d/dx[sinx]

cosx

d/dx[cosx]

-sinx

d/dx[tanx]

sec²x

d/dx[cscx]

-cscxcotx

d/dx[secx]

secxtanx

d/dx[cotx]

-csc²x

∫1/(a²+x²)dx

(1/a)tan^-1(x/a) + C

d/dx[sin^-1x]

1/√(1-x²)

d/dx[cos^-1x]

-1/√(1-x²)

d/dx[tan^-1x]

1/(1+x²)

d/dx[cot^-1x]

-1/(1+x²)

d/dx[sec^-1x]

1/[x√(x²-1)]

d/dx[csc^-1x]

-1/[x√(x²-1)]

∫(1/x)dx

ln|x| + C

∫e^xdx

e^x + C

∫a^xdx

e^x/lna + C

∫lnxdx

xlnx - x + C

∫sinxdx

-cosx + C

∫cosxdx

sinx + C

∫tanxdx

-ln|cosx| + C

∫cotxdx

ln|sinx| + C

∫secxdx

ln|secx+tanx| + C

∫cscxdx

ln|cscx-cotx| + C

∫sec²xdx

tanx + C

∫secxtanxdx

secx + C

∫csc²xdx

-cotx + C

∫tan²xdx

tanx-x + C

sin²x + cos²x =

1

1 + tan²x =

sec²x

1 + cot²x =

csc²x