Answer
$f'(\theta)=10\tan{5\theta}\sec^2{5\theta}.$
Work Step by Step
$u=\tan{5\theta}$; $\dfrac{du}{d\theta}=5\times\sec^2{5\theta}=5\sec^2{5\theta}.$
$\dfrac{d}{du}f(u)=2u$
$\dfrac{d}{d\theta}f(\theta)=\dfrac{d}{du}f(u)\times\dfrac{du}{d\theta}=2\tan{5\theta}\times5\sec^2{5\theta}=10\tan{5\theta}\sec^2{5\theta}.$
