Question

If $y=x^x$, then find $\frac{dy}{dx}$

Answer 1

We have, $y=x^x$

Taking $\log$ on both the sides, we get
$\log y=x\log x$
On differentiating w.r.t. $x$, we get
$\frac{1}{y}\frac{dy}{dx}=\frac{x}{x}+\log x$
$\Rightarrow \frac{dy}{dx}=y+y\log x$
$\Rightarrow \frac{dy}{dx}=x^x(1+\log x)$ ....$(\because y=x^x)$