Question

Find derivative of $x^x:$

Answer 1

Let $y=x^x$

Applying log on both sides

$\log y=x\log x$

Differentiating wrt x

$\frac{1}{y}\frac{dy}{dx}=\log x+\frac{1}{x}\times x$

$\frac{dy}{dx}=y(1+\log x)$

$\frac{dy}{dx}=x^x(1+\log x)$