## Calculus (3rd Edition)

Recall that $(e^x)'=e^x$ Since we have $$f(x)= e^{e^x}$$ then the derivative $f'(x)$, using the chain rule, is given by \begin{align*}f'(x)&=e^{e^x} (e^x)'\\ &=e^x e^{e^x} . \end{align*}