alleryIf $y_n$ denotes the $n$-th derivative of $y = \sin x$, then $y_n = $:
A$\sin(x + n\pi/2)$
B$\sin(x + n\pi)$
C$\sin x \cdot n!$
D$\cos(x + n\pi/2)$
Answer & Solution
Correct answer: A. $\sin(x + n\pi/2)$
Each differentiation of sin shifts phase by $\pi/2$: $y_1 = \sin(x + \pi/2) = \cos x$
$y_2 = \sin(x + \pi) = -\sin x$, etc. General: $y_n = \sin(x + n\pi/2)$.
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