Derivatives and Integrations

AP Calculus AB

d/dx log_au

1/ulna du/dx

d/dx sec u

sec u tan u du/dx

d/dx csc u

-csc u cot u du/dx

d/dx sin u

cos u du/dx

d/dx cos u

-sin u du/dx

d/dx tan u

sec² u du/dx

d/dx cot u

-csc^2 u du/dx

uv'+vu'

d/dx (uv)

vu'-uv'/v²

d/dx (u/v)

d/dx xⁿ

nx^n-1

d/dx e^u

e^u du/dx

d/dx a^u

a^ulna du/dx

d/dx lnu

1/u du/dx

d/dx c (if c is a constant)

0

∫uⁿ du

uⁿ⁺¹/n+1 + C

∫sec²u du

tan u + C

∫a^u du

a^u/lna + C

∫sin u du

-cos u + C

∫cos u du

sin u + C

∫du/u

ln |u| + C

∫csc²u du

cot u + C

∫e^u du

e^u + C