TITLE: Evaluating the derivative of $\large \;e^{e^x}$?
QUESTION [12 upvotes]: I know that the derivative of $\,e^x\,$ is $\,e^x$.
But how do I evaluate $\dfrac{d}{dx}{\large\left(e^{e^x}\right)}\,$?

REPLY [6 votes]: Here's another method: for any positive function $f$, its derivative equals the function $f$ times its logarithmic derivative. In our case $f(x)=e^{e^x}$, so its logarithm, $e^x$, has derivative $e^x$.