Product Rule

103. Product Rule

\frac{𝑑}{𝑑 𝑥} [𝑓 (𝑥) 𝑔 (𝑥)] = 𝑓^{'} (𝑥) 𝑔 (𝑥) + 𝑓 (𝑥) 𝑔^{'} (𝑥)

Example

\frac{𝑑}{𝑑 𝑥} [𝑥^{2} sin (𝑥)]

\begin{matrix} 𝑓 (𝑥) = 𝑥^{2} 𝑔 (𝑥) = sin (𝑥) \\ 𝑓^{'} (𝑥) = 2 𝑥 𝑔^{'} (𝑥) = cos (𝑥) \end{matrix}

\frac{𝑑}{𝑑 𝑥} [𝑥^{2} sin (𝑥)] = 2 𝑥 sin (𝑥) + 𝑥^{2} cos (𝑥)