AP Calculus Formulas

Integrals and Derivative Formulas

d/dx[cu]

cu’

d/dx[u±v]

u’ ± v'

d/dx[uv] Product Rule

uv’+vu’

d/dx[u/v] Quotient Rule

(v u' - u v') / v^2

d/dx[c]

0

d/dx[u^n] Power Rule

n u^{n-1} u'

d/dx[x]

1

d/dx[ |u| ]

u/|u| * u’

d/dx[ln u]

u’/u

d/dx[e^u]

e^u * u’

d/dx[log a u]

u’/(u ln a)

d/dx[a^u]

(ln a)a^u u’

d/dx[sin u]

cos u 

d/dx[cos u]

-(sin u)

d/dx[tan u]

(sec²u)

d/dx[cot u]

-(csc²u)

d/dx[sec u]

(sec u tan u)

d/dx[csc u]

-(csc u cot u)

d/dx[arcsin u]

u’ / sqrt(1-u²)

d/dx[arccos u]

-u’ / sqrt(1-u²)

d/dx[arctan u]

u’ / (1+u²)

d/dx[arccot u]

-u’ / (1+u²)

d/dx[arcsec] u

u’ / |u| sqrt(u²-1)

d/dx[arccsc u]

-u’ / |u|*sqrt(u²-1)

∫kf(u) du

k*∫f(u) du

∫[f(u) +- g(u)]du

∫f(u) du +- ∫g(u) du

∫du

u + C

∫u^n du

u^n+1 / n+1 +C

∫du/u

ln|u| + C

∫e^u du

e^u + C

∫a^u du

(1/ln(a)) a^u + C

∫sin u du

-cos u + C

∫cos u du

sin u + C

∫tan u du

-ln|cos u| + C

∫cot u du

ln|sin u| + C

∫sec u du

ln|sec u + tan u| + C

∫csc u du

-ln|csc u + cot u| + C

∫sec²u du

tan u + C

∫csc²u du

-cot u + C

∫sec u tan u du

sec u + C

∫csc u cot u du

-csc u + C

∫du/ sqrt(a²-u²)

arcsin u/a + C

∫du / a²+u²

1/a * arctan u/a +C

∫du/ u sqrt(u²-a²)

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