DIFFERENTIATION RULES

Here are the most important differentiation rules, written in differential notation.

• To get the ordinary version of these rules, divide both sides by du.
• To get the chain rule version of these rules, divide both sides by dx.

duⁿ = nu^n-1 du
de^u = e^u du
d sin u = cos u du
d cos u = –sin u du
d ln u = u^-1 du

d tan u = 1/cos²u du
d sin^-1u = (1–u²)^-1/2 du
d tan^-1u = (1+u²)^-1 du

d(u+cv) = du + c dv
d(uv) = u dv + v du
d(u/v) = (v du – u dv)/v²

(u and v are functions and c is a constant)