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If y=e^(x).cotx then (dy)/(dx) will be...

If `y=e^(x).cotx` then `(dy)/(dx)` will be

A

`e^(x) cot x- cosec^(2) x`

B

`e^(x) cosec^(2) x`

C

`e^(x)[cot x- cosec^(3) x]`

D

`e^(x) cot x`

Text Solution

Verified by Experts

The correct Answer is:
C
`y=e_(x),(d)/(dx)cotx`
`(dy)/(dx)=e_(x)(cot x)+cot x(d)/(dx)(e_(x))`
`=e_(x)(-cosec_(2)x)+ cot x e_(x)`
`= e_(x)[cor x- cosec_(2) x]`.
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