How does one use logarithmic differentiation to differentiate this function:
f(x) = x^x
$\displaystyle \ln\text{ }f=x\ln(x)$ so that $\displaystyle \frac{f'}{f}=1+\ln(x)$ and so $\displaystyle f'=f\left(1+\ln(x)\right)$, but $\displaystyle f=x^x$ and so $\displaystyle f'=x^x\left(1+\ln(x)\right)$