How to differentiate $x^{\log(x)}$? I want to differentiate $x^{\log(x)}$ with respect to $x$.
By using chain rule ($x{log(x)}\frac{1}{x}$), I got the answer $\log x$. Is it right?

Assuming $\log x$ is base $e$, let $y=x^{\log x}$. Take a logarithm of both sides to get $ \log y = \log (x^{\log x}) = \log x \log x$. Differentiate both sides to get $\frac{y'}{y}= \frac{2 \log x}{x} $  Multiplying by $y$ gives $y'=x^{\log x}\frac{2 \log x}{x}$
