Home » Blog » Find the derivative of xx

Find the derivative of xx

Find the derivative of the following function:

    \[ f(x) = x^x. \]


We can take differentiate using logarithmic differentiation. First, take the logarithm of both sides,

    \[ \log f(x) = \log x^x  = x \log x. \]

Then, differentiating we obtain

    \begin{align*}  &&\frac{f'(x)}{f(x)} &= 1+ \log x  \\ \implies && f'(x) &= f(x) ( 1+ \log x) \\ \implies && f'(x) &= x^x (1 + \log x). \end{align*}

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):