Question

Find the derivative of x^x

Answer 1

$y = x^x \\ =e^{x.logx}$

now differentiate with respect to x 
$\frac{dy}{dx} =e^{x.logx}.\frac{d(xlogx)}{dx} \\ =e^{x.logx}.({x\frac{logx}{dx}+logx.\frac{dx}{dx})} \\= e^{x.logx}(1+logx)$