alleryIf $y = \sin(\cos x)$, then $\dfrac{dy}{dx}$ equals:
A$-\cos(\cos x) \cdot \sin(\cos x)$
B$-\sin x \cos(\cos x)$
C$\sin x \cdot \cos(\cos x)$
D$\cos(\cos x)$
Answer & Solution
Correct answer: B. $-\sin x \cos(\cos x)$
Chain rule: $dy/dx = \cos(\cos x) \cdot d/dx(\cos x) = \cos(\cos x) \cdot (-\sin x) = -\sin x \cos(\cos x)$.
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