AP cal Ab derivatives to know

constant

0

power rule

d/dx x^n = nx^n-1

product rule

d/dx f(x)*g(x) = f(x)g’(x) + g(x)f’(x)

quotient rule

d/dx f(x)/g(x) = g(x)f’(x) - f(x)g’(x) / g(x)²

chain rule

d/dx f(g(x)) = f’(g(x))*g’(x)

d/dx sin^-1u

d/dx sin^-1u = u’/sqrroot 1-u²

d/dx tan^-1u

u’/1+u²

sinu

cosudu

cosu

-sinudu

tanu

sec²udu

cotu

-csc²udu

secu

secutanudu

cscu

-cscucotudu

e^g(x)

e^g(x) * g’(x)

lng(x)

g’(x)/g(x)

a^g(x)

lna * a^g(x) * g’(x)

log a g(x)

g’(x)/lna g(x)