Differentiate $d/dxe^(e^(2x))$ ?

Question

(i mean expotential power expotential power 2x)

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Answer 1 · 2017-08-15T03:10:08

$2e^((e^(2x)+2x))$

For this problem we shall use the chain rule along with the standard differential of $e^x$ as follows:

$d/dx e^f(x) = e^f(x)* d/dxf(x)$

In our example $f(x) = e^(2x)$

Hence, $d/dx e^(e^(2x) )= e^(e^(2x) )* d/dx e^(2x)$

$=e^(e^(2x) )* e^(2x) *d/dx 2x$

$=e^(e^(2x) )* e^(2x) *2$

$=2e^((e^(2x)+2x))$