If h(x) = f(x)g(x) for all x, the nth derivative of h is given by

where the coefficients $\left(\begin{array}{c}n\\ r\end{array}\right)$ are binomial coefficients.

For example, to find h⁽⁸⁾(x), when h(x) = x² sin x, let f(x) = x² and g(x) = sin x. Then f′(x) = 2x and f″(x) = 2, with higher derivatives being zero; and g⁽⁸⁾(x) = sinx, g⁽⁷⁾(x) = −cosx and g⁽⁶⁾ (x) = −sinx. So