AP Calculus AB Important Integrals/Derivatives

d/dx cos x =

-sin x

d/dx sec x =

sec x tan x

d/dx tan x =

sec^2 x

d/dx cot x =

- csc^2 x

d/dx csc x =

- csc x cot x

d/dx sin x =

cos x

∫ csc u du =

-ln |csc u + cot u| + C

∫ sec u du =

ln |sec u + tan u| + C

∫ cot u du =

ln |sin u| + C

∫ tan u du =

-ln |cos u| + C

∫ sin u du =

-cos u + C

∫ cos u du =

sin u + C

∫ a^x dx =

(1/ln a) * a^x + C

d/dx (log_a u) =

(1/ln a) (1/u) u'

d/dx (a^u) =

(ln a) a^u du/dx

d/dx (ln x) =

1/x

∫ (1/x) dx =

ln |x| + C

d/dx (e^x) =

e^x

∫ e^x dx =

e^x + C

d/dx arcsin u =

u' / √(1 - u^2)

d/dx arctan u =

u' / (1 + u^2)

d/dx arcsec u =

u' / (|u| * √(u^2 - 1))

d/dx arccos u =

- u' / √(1 - u^2)

d/dx arccot u =

- u' / (1 + u^2)

d/dx arccsc =

- u' / (|u| * √(u^2 - 1))

∫ du / √(a^2 - u^2) =

arcsin (u/a) + C

∫ du / (a^2 - u^2) =

(1/a) * arctan (u/a) + C

∫ du / (u * √(a^2 - u^2)) =

(1/a) * arcsec (|u| / a) + C

Continuous Interest Formula

A = Pe^rt

Compound Interest Formula

Y = P * (1 + (r/n))^nt

Inverse Derivative Formula

g'(x) = 1 / f'(g(x))