If $ y=\frac{e^{2 x} \cos x}{x \sin x} $, then $ \frac{d y}{d x} $ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

y=\frac{e^{2 x} \cos x}{x \sin x}

, then

\frac{d y}{d x}

is equal to

View answer and explanation

Correct option: A

\frac{e^{2 x}\left[(2 x-1) \cot x-x \operatorname{cosec}^{2} x\right]}{x^{2}}

Option A is correct because the derivative is found using logarithmic differentiation and simplifying the resulting expression.

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