Find the indicated derivative.
-Find $y ( 4 )$ if $y = - 6 \cos x$.
A) $y ( 4 ) = 6 \cos x$
B) $y ^ { ( 4 ) } = - 6 \sin x$
C) $y ^ { ( 4 ) } = - 6 \cos x$
D) $y ( 4 ) = 6 \sin x$

Question

Quizplus · Accepted Answer

The derivative of $y = -6\cos x$ is $y' = 6\sin x$.
Taking the derivative again, we have $y'' = 6\cos x$.
Taking the derivative a third time, we have $y''' = -6\sin x$.
And finally, taking the derivative a fourth time, we have $y^{(4)} = -6\cos x$.
Therefore, $y^{(4)}$ is equal to $-6\cos x$, so the correct choice is C.

To find $y(4)$, we need to evaluate the expression $y$ at $x=4$. Plugging in, we get $y(4) = -6\cos 4$ which is a numerical value, and not one of the answer choices. Therefore, none of the answer choices are correct for this part of the question.

Find the Indicated Derivative y(4)y ( 4 )y(4) If y=−6cos⁡xy = - 6 \cos xy=−6cosx

Find the Indicated Derivative $y ( 4 )$ If $y = - 6 \cos x$