Question

If $y=\ln \left(x^{e^x}\right)$ find $\frac{dy}{dx}$.

Answer 1

Given,

$y=\ln \left(x^{e^x}\right)$

or, $y=e^x\ln x$

Now differentiating both sides with respect to $x$ we get,

$\frac{dy}{dx}=e^x\ln x+\frac{e^x}{x}$.