What is $\frac{d}{dx}\left(e^{x} \log x\right)$ for $x > 0$?

Explanation

1. 01

   Product rule: $(e^{x})'\log x + e^{x}(\log x)'$.

2. 02

   $e^{x}\log x + \frac{e^{x}}{x} = e^{x}\left(\log x + \frac{1}{x}\right)$.