If y=(x cot^(3)x)^(3/2), then (dy)/(dx)=...

If `y=(x cot^(3)x)^(3/2)`, then `(dy)/(dx)=`

A

`3/2 (x cot^3 x)^(1//2)[cot^3 x-3x cot^2x" cosec"^2x]`

B

`3/2 (x cot^3 x)^(1//2)[cot^2 x-3x cot^2x" cosec"^2x]`

C

`3/2 (x cot^3 x)^(1//3)[cot^3 x-3x" cosec"^2x]`

D

`3/2 (x cot^3 x)^(3//2)[cot^3 x-3x" cosec"^2x]`

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The correct Answer is:

A

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