I don't understand this question. I realize that
$$\log_A x = \ln X/\ln A,$$
but when I substitute that and take the derivative, I get
$$y' = e^{\left(\ln x\right)^2/10}\cdot\frac{2\ln x}{\ln 10}\cdot\frac{1}{x}.$$
How do I continue from here? What is the derivative of $$f(x) = x^{\log_{10} x}?$$
EDIT: I see how Raymond got his answer but my book says this is $$y' = x^{\log_{10} x}\cdot\frac{ln 10\cdot\log_{10} x + ln x} {x\cdot\ln 10}.$$ So how can one get this answer?