Differentiation (and Integration) Rules

DIFFERENTIATION (AND INTEGRATION) 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.
To get the corresponding integration rule, simply put an integral sign in front of each side.

duⁿ = nuⁿ⁻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)