Answer:
f'(x) = 18x sin²(3x²)cos(3x²)
Step-by-step explanation:
Differentiate using the chain rule
Given
h(x) = f(g(x)) , then
h'(x) = f'(g(x)) × g'(x) ← Chain rule
Here
f(x) = sin³(3x²)
f'(x) = 3sin²(3x²)cos(3x²)
g(x) = 3x²
g'(x) = 6x
Thus
F'(x) = 3sin²(3x²)cos(3x²) × 6x
= 18x sin²(3x²)cos(3x²)
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