we have:

First thing we do: $ Ln (y) = Ln(10x) * Ln(10x) $

Finally after applying the "rules" : $ y' = y* [ \frac {2 Ln (10x)}{x} ] $

Am I correct? Because wolfram alpha gives the answer in a different form first derivative of y= 10x^(Ln10x) - Wolfram|Alpha