Derivative of e^(e^x)

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 / x\
 \E /
E

e^{e^{x}}

E^(E^x)

Detail solution

Let $u = e^{x}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} e^{x}$ :
1. The derivative of $e^{x}$ is itself.
The result of the chain rule is:

$e^{e^{x}} e^{x}$
Now simplify:

$e^{x + e^{x}}$

The answer is:

e^{x + e^{x}}

The first derivative [src]

    / x\
 x  \E /
e *e

e^{e^{x}} e^{x}

Simplify

The second derivative [src]

             / x\
/     x\  x  \E /
\1 + e /*e *e

\left(e^{x} + 1\right) e^{e^{x}} e^{x}

Simplify

The third derivative [src]

                      / x\
/       x    2*x\  x  \E /
\1 + 3*e  + e   /*e *e

\left(e^{2 x} + 3 e^{x} + 1\right) e^{e^{x}} e^{x}

Simplify