Answer
$f'(x) = (1-3e^{3x})e^{x-e^{3x}}$
Work Step by Step
In order to derivate this function you have to apply the chain rule
Let's make a «u» substitution to make it easier
$f(u) = e^u$
$u=x-e^{3x}$
Derivate the function:
$f'(u) = u'e^u$
Now let's find u'
*Note: Here you have to apply the chain rule again
$u' = 1 - 3e^{3x}$
Then undo the substitution, simplify and get the answer:
$f'(x) = (1-3e^{3x})e^{x-e^{3x}}$
