Method of Differentiation
Higher Order Derivatives
Premium Question
Grade 12
Question:
If $y = \sin(\sin x)$, then $y'' + y' \tan x + y \cos^2 x$ equals:
(1) $0$
(2) $1$
(3) $\sin x$
(4) $\cos x$
Step-by-Step Solution
Key Concept: Compute $y' = \cos(\sin x) \cos x$ and $y''$ explicitly in terms of $\sin(\sin x)$ and $\cos(\sin x)$, then substitute all three terms together and look for cancellation.
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Correct Answer: (1)