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^(2) x "cosec"^(2)x)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:

A

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