Exercise 9.3

We expand the 2nd term of Eq. (9.17) using the product rule: \[ \begin{flalign*} [\mathrm{V}(x), \mathrm{P}]\psi(x) &= V(x)(-\mathrm{i} \hbar \frac{\mathrm{d}}{\mathrm{d}x})\psi(x) - (-\mathrm{i} \hbar \frac{\mathrm{d}}{\mathrm{d}x}) V(x) \psi(x)&\\ &= V(x)(-\mathrm{i} \hbar \frac{\mathrm{d}}{\mathrm{d}x}) \psi(x) + \mathrm{i} \hbar \frac{\mathrm{d}}{\mathrm{d}x} V(x) \psi(x) + \mathrm{i} \hbar \frac{\mathrm{d}}{\mathrm{d}x} \psi(x) V(x)\\ &= \mathrm{i} \hbar \frac{\mathrm{d}}{\mathrm{d}x} V(x) \psi(x) \end{flalign*} \] \[ \Rightarrow [\mathrm{V}(x), \mathrm{P}] = \mathrm{i} \hbar \frac{\mathrm{d}}{\mathrm{d}x} V(x) \]