$y=10 x^{\ln(10x)}=10 \exp(\ln(x)\ln(10x))$

$\dfrac {dy}{dx}=10\exp(\ln(x)\ln(10x))\times \dfrac {d}{dx}\left(\ln(x)\ln(10x)\right)=$

$10\exp(\ln(x)\ln(10x))\times\left(\dfrac 1 x \ln(10x)+\ln(x)\dfrac{10}{x}\right)=$

$10^{\ln(10x)} \left(\dfrac 1 x \ln(10x)+\ln(x)\dfrac{10}{x}\right)$

This is what Mathematica gives.. I 'm sure this an the various forms wolfram alpha gives are all equivalent.