Find the indicated derivative.
-Find $y ^ { \prime \prime \prime }$ if $y = 6 x \sin x$.
A) $y ^ { \prime \prime \prime } = - 6 x \cos x - 18 \sin x$
B) $y ^ { \prime \prime \prime } = 12 \cos x - 6 x \sin x$
C) $y ^ { \prime \prime \prime } = - 6 x \cos x + 18 \sin x$
D) $y ^ { \prime \prime \prime } = 6 x \cos x + 18 \sin x$

Question

Quizplus · Accepted Answer

To find the third derivative of $y = 6x\sin x$, we apply the product rule and the chain rule. First derivative: $y' = 6\sin x + 6x\cos x$. Second derivative: $y'' = 6\cos x + 6\cos x - 6x\sin x = 12\cos x - 6x\sin x$. Third derivative: $y''' = -12\sin x - 6\sin x - 6x\cos x = -18\sin x - 6x\cos x$.

Find the Indicated Derivative y′′′y ^ { \prime \prime \prime }y′′′

Find the Indicated Derivative $y ^ { \prime \prime \prime }$