If y = e^x . cot x then $\frac{d y}{d x}$ will be

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e^xcot x

e^x cosec²x

e^x[cot x – cosec²x]

e^xcot x – cosec²x

answer is C.

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Detailed Solution

$\begin{array}{l} y = e^{x} \cdot \cot x \\ \frac{d y}{d x} = e^{x} \frac{d}{d x} (\cot x) + \cot x \frac{d}{d x} (e^{x}) \\ = e^{x} (- {cosec}^{2} x) + \cot x e^{x} \\ = e^{x} [cotx - {cosec}^{2} x] \end{array}$

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