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Basic Differentiation Rule

If y=ex. x th...

Question

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

A

e^{x} cot x - c o s e c x

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B

e^{x} ({cot}^{2} x - c o s e c^{2} x)

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C

e^{x} (cot x - c o s e c^{2} x)

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D

e^{x} cot x - c o s e c^{2} x

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Solution

The correct option is C $e^{x} (cot x - c o s e c^{2} x)$
$y = e^{x} . c o t x \frac{d y}{d x} = e^{x} \frac{d}{d x} (c o t x) + c o t x \frac{d}{d x} (e^{x}) = e^{x} (- c o s e c^{2} x) + c o t x (e^{x}) = e^{x} [c o t x - c o s e c^{2} x]$

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