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JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1
Let f(x)=1+sin⁡(3x)⋅g(x)f(x)=1+\sin (3 x) \cdot g(x) where g(x)g(x) is differentiable, then f′(0)f^{\prime}(0) is
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Correct option: B
3g(0)3 g(0)
Option B (3g(0)3 g(0)) is correct because the derivative f′(x)f'(x) is calculated using the product rule and then evaluated at x=0x=0.

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