Differentiate $x^{3} \log x$ with respect to $x$.

Explanation

1. 01

   Product rule: $(uv)' = u'v + uv'$, with $u = x^{3}$ and $v = \log x$.

2. 02

   $(3 x^{2})(\log x) + (x^{3})(\frac{1}{x}) = 3 x^{2} \log x + x^{2}$.