# How do you find the derivative of f(x)= x^logx?

$f \left(x\right) = {e}^{\log x \cdot \ln x}$ hence

d(f(x))/dx=e^(logx*lnx)*(logx*lnx)'=e^(logx*lnx)*(1/x*lnx+logx/x)= x^(logx)*(lnx/x+logx/x)

Convert from one base to the other using the formulae

$\ln \left(x\right) = \log \frac{x}{\log} \left(e\right)$

$\log \left(x\right) = \ln \frac{x}{\ln} \left(10\right)$