Question

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

Answer 1

`f(x)=e^(logx*lnx)` 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(x) = log(x) / log(e)`

`log(x) = ln(x) / ln(10)`