Implicit Derivatives AP Calc AB

d/dx(cu)

cu′

d/dx(u ± v)

u′ ± v′

d/dx(uv)

u′v + uv′

d/dx(u/v)

(vu′ − uv′)/v²

d/dx(c)

0

d/dx(x)

1

d/dx(uⁿ)

nuⁿ⁻¹u′

d/dx(eᵘ)

eᵘu′

d/dx(ln u)

u′/u

d/dx(sin u)

(cos u)u′

d/dx(cos u)

−(sin u)u′

d/dx(tan u)

(sec² u)u′

d/dx(cot u)

−(csc² u)u′

d/dx(sec u)

(sec u tan u)u′

d/dx(csc u)

−(csc u cot u)u′

d/dx(arcsin u)

u′/√(1 − u²)

d/dx(arccos u)

−u′/√(1 − u²)

d/dx(arctan u)

u′/(1 + u²)

d/dx(arccot u)

−u′/(1 + u²)

d/dx(arcsec u)

u′/(|u|√(u² − 1))

d/dx(arccsc u)

−u′/(|u|√(u² − 1))