Two functions: (fg)' = f'g + fg'

Three functions: (fgh)' = f'gh + fg'h + fgh' Pattern: differentiate one factor at a time, keep the rest.

n functions: (f1f2...fn)' = sum over i of [f1...fi'...*fn]

Alternative for products: Use logarithmic differentiation. y = f1 * f2 * ... * fn ln y = ln f1 + ln f2 + ... + ln fn (1/y)*y' = f1'/f1 + f2'/f2 + ... + fn'/fn y' = y * (f1'/f1 + f2'/f2 + ... + fn'/fn)

This is often faster than direct product rule for 3+ factors.

Example: y = (x+1)(x+2)(x+3) y'/y = 1/(x+1) + 1/(x+2) + 1/(x+3) y' = (x+1)(x+2)(x+3) * [1/(x+1) + 1/(x+2) + 1/(x+3)]