R Notebook

\[ \frac{d}{dx} (x\log x-x) \\ = -(\frac{d}{dx}(x))+\frac{d}{dx}(x\log(x)) \\ = -1 + \log(x) \frac{d}{dx}(x) + x \frac{d}{dx}(\log (x)) \\ = -1 + x (\frac{x}{dx}(\log(x)))+1 \log (x) \\ = -1 + \log(x) + \frac{1}{x}x \\ = \log (x) \]