Math basics › Calculus
Derivative rules
Power rule
d/dx of xⁿ is n·xⁿ⁻¹. Bring the power down, knock one off.
Product and quotient
(uv)′ = u′v + uv′. (u/v)′ = (u′v − uv′)/v² — the order on top matters.
Chain rule
Derivative of the outside, leaving the inside alone, times the derivative of the inside. The forgotten inside derivative is the most common mistake in all of calculus.
The ones to memorise
sin′ = cos, cos′ = −sin, (eˣ)′ = eˣ, (ln x)′ = 1/x.