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 $\frac{1}{y}$*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 = $\frac{1}{x+1}$ + $\frac{1}{x+2}$ + $\frac{1}{x+3}$ y' = (x+1)(x+2)(x+3) * [$\frac{1}{x+1}$ + $\frac{1}{x+2}$ + $\frac{1}{x+3}$]