Answer
$y'=2[\tan(\sin\theta)][\sec^{2}(\sin\theta)]\cos\theta$
Work Step by Step
$y=\tan^{2}(\sin\theta)$
Start the differentiation process by using the chain rule:
$y'=2[\tan(\sin\theta)][\tan(\sin\theta)]'=...$
Apply the chain rule one more time to evaluate the indicated derivative:
$...=2[\tan(\sin\theta)][\sec^{2}(\sin\theta)](\sin\theta)'=...$
Evaluate the remaining derivative and simplify:
$...=2[\tan(\sin\theta)][\sec^{2}(\sin\theta)]\cos\theta$
