\begin{align*} \frac{d \frac{p \cdot V}{n \cdot R}}{dV} = \frac{d}{dV} \left[ \frac{pV}{nR} \right] = \frac{1}{nR} \left( \frac{d}{dV} [p V] \right) \end{align*} (provided that $n$ and $R$ are independent of $V$). Now using the product rule treating $p$ and $V$ as functions of $V$ gets you the desired result: \begin{align*} \frac{1}{nR} \left( \frac{d}{dV} [p V] \right) = \frac{1}{nR} \left(\frac{dp}{dV} \cdot V + p \cdot \frac{dV}{dV} \right) = \frac{dp}{dV} \frac{V}{nR} + \frac{p}{nR} \frac{dV}{dV} \end{align*}