Find dy/dt.
-$$y = \cos ^ { 3 } ( \pi t - 12 )$$
A) $- 3 \cos ^ { 2 } ( \pi t - 12 ) \sin ( \pi t - 12 )$
B) $- 3 \pi \sin ^ { 2 } ( \pi t - 12 )$
C) $3 \cos ^ { 2 } ( \pi t - 12 )$
D) $- 3 \pi \cos ^ { 2 } ( \pi t - 12 ) \sin ( \pi t - 12 )$

Question

Quizplus · Accepted Answer

We use the chain rule and simplify as follows:
$$\frac{dy}{dt} = \frac{d}{dt}\left(\cos^3(\pi t - 12)\right)$$
$$= -3\cos^2(\pi t - 12)\sin(\pi t - 12)\cdot(\pi)$$
$$= -3\pi\cos^2(\pi t - 12)\sin(\pi t - 12)$$
Therefore, the correct answer is D.

Find Dy/dt y=cos⁡3(πt−12)y = \cos ^ { 3 } ( \pi t - 12 )y=cos3(πt−12)

Find Dy/dt $y = \cos ^ { 3 } ( \pi t - 12 )$