For , which of the following equals…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For f(x)=ln⁡(3x) sin⁡(2x) exf(x)=\ln(3x)\,\sin(2x)\,e^{x}, which of the following equals f′(x)f'(x)? (a) ex[sin⁡(2x)x+2ln⁡(3x)cos⁡(2x)]e^{x}\left[ \dfrac{\sin(2x)}{x} + 2\ln(3x)\cos(2x) \right] (b) ex[sin⁡(2x)x+2ln⁡(3x)cos⁡(2x)+ln⁡(3x)sin⁡(2x)]e^{x}\left[ \dfrac{\sin(2x)}{x} + 2\ln(3x)\cos(2x) + \ln(3x)\sin(2x) \right] (c) ex[sin⁡(2x)x+2cos⁡(2x)+ln⁡(3x)sin⁡(2x)]e^{x}\left[ \dfrac{\sin(2x)}{x} + 2\cos(2x) + \ln(3x)\sin(2x) \right] (d) ex[sin⁡(2x)x+ln⁡(3x)cos⁡(2x)+ln⁡(3x)sin⁡(2x)]e^{x}\left[ \dfrac{\sin(2x)}{x} + \ln(3x)\cos(2x) + \ln(3x)\sin(2x) \right]

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