# Product Law of Differentiation

## Formula

General form
$\dfrac{d}{dx}{\Big({f(x)}.{g(x)}\Big)}$ $\,=\,$ ${g(x)}\dfrac{d{f(x)}}{dx}$ $+$ ${f(x)}\dfrac{d{g(x)}}{dx}$
Leibniz’s notation
$\dfrac{d}{dx}{(u.v)}$ $\,=\,$ $v.\dfrac{du}{dx}$ $+$ $u.\dfrac{dv}{dx}$
Differentials Notation
$d{(u.v)}$ $\,=\,$ $v.du$ $+$ $u.dv$

### Proof

Learn how to derive the property of product rule of differentiation in differential calculus.