alleryUsing the CHAIN rule, d/dx [sin(3x)] equals:
A$\cos(3x)$ (forgetting the chain rule)
B$3 \cos(3x)$ (chain rule, inner derivative is 3)
C$\cos(x)$ (incorrect simplification of arg)
D$3 \cos(x)$ (incorrectly mixing variables)
Answer & Solution
Correct answer: B. $3 \cos(3x)$ (chain rule, inner derivative is 3)
**Chain rule:** outer derivative × inner derivative. Outer: sin(u) → cos(u).
**Inner:** 3x → 3. So d/dx [sin(3x)] = cos(3x) × 3 = 3 cos(3x).
Don't forget to multiply by the inner derivative!
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