Answer
$$ f'(x)=-6e^{5-6x}\sec^2 (e^{5-6x})$$
Work Step by Step
Recall that $(e^x)'=e^x$
Recall that $(\tan x)'=\sec^2 x$.
Since we have
$$ f(x)= \tan(e^{5-6x})$$
then the derivative $ f'(x)$, using the chain rule, is given by
$$ f'(x)=\sec^2 (e^{5-6x})(e^{5-6x})'=-6e^{5-6x}\sec^2 (e^{5-6x})$$
