Derivatives and Antiderivatives to Know

d/dx (sin x)

cos x

d/dx (cos x)

-sin x

d/dx (tan x)

sec²x

d/dx (cot x)

-csc²x

d/dx (sec x)

secxtanx

d/dx (csc x)

-cscxcotx

d/dx (a ⋅ xⁿ)

nax^n-1

d/dx (e^x)

e^x

d/dx (sin^-1x)

d/dx (cos^-1x)

d/dx (tan^-1x)

d/dx (ln x)

d/dx (log_bx)

d/dx (k)

0

d/dx (f(x) ⋅ g(x))

f(x)g’(x) + g(x)f’(x)

d/dx [f(x)/g(x)]

d/dx (f(g(x)))

f’(g(x)) ⋅ g’(x)

d/dx (a^x) where a is a constant

∫auⁿ ⋅ du

∫0 ⋅ du

c

∫du

u + c

∫1/u ⋅ du

ln |u| + c

∫e^u ⋅ du

e^u + c

∫ln u ⋅ du

u ln u - u + c

∫cos u ⋅ du

sin u + c

∫sin u ⋅ du

-cos u + c

∫sec²u ⋅ du

tan u + c

∫csc²u ⋅ du

-cot u + c

∫tan u ⋅ sec u ⋅ du

sec u + c

∫cot u ⋅ csc u ⋅ du

-csc u + c

∫tan u ⋅ du

-ln |cos u| + c

∫sec u ⋅ du

ln |sec u + tan u| + c

tan^-1u + c

sin^-1u + c