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?

$$y=x^{\log x}$$
$$\log y=\log x \log x=\log^2 x$$
$$\frac{y'}{y}=\frac{2}{x}\log x$$
$$y'=\frac{2y}{x}\log x$$
$$y'=2\frac{x^{\log x}}{x}\log x$$
$$y'=2x^{\log x-1}\log x$$
