If $y = \cos^3(\sec^2 2t)$, find $\frac{dy}{dt}$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $-12 \cos^2(\sec^2 2t) \sin(\sec^2 2t) \sec^2(2t) \tan(2t)$ ##
$y = \cos^3(\sec^2 2t)$
Applying chain rule,
$\frac{dy}{dt} = 3\cos^2(\sec^2 2t) \times [-\sin(\sec^2 2t)] \times 2\sec 2t \times \sec 2t \tan 2t \times 2$
$= -12 \cos^2(\sec^2 2t) \times \sin(\sec^2 2t) \times \sec^2 2t \times \tan 2t$