# What are the critical points of f(x) =ln(xe^x)?

The function is defined only for $x > 0$ and using the properties of logarithms:
$\ln \left(x {e}^{x}\right) = \ln x + \ln \left({e}^{x}\right) = x + \ln x$
$\frac{d}{\mathrm{dx}} \ln \left(x {e}^{x}\right) = 1 + \frac{1}{x} \ne 0$ for $x > 0$