Method of Differentiation
Higher Order Derivatives
Premium Question
Grade 12
Question:
If $f(x) = \sin(\ln x)$, the value of $x^2 f''(x) + xf'(x) + f(x)$ equals _____.
Step-by-Step Solution
Key Concept: Compute $f'(x)$ and $f''(x)$ directly using the chain rule, keeping every term as a multiple of $\sin(\ln x)$, $\cos(\ln x)$ and a power of $x$ — then combine and simplify.
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Correct Answer: 0