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If xy = tan^(-1) (xy) + cot^(-1) (xy), ...

If ` xy = tan^(-1) (xy) + cot^(-1) (xy), " then" (dy)/(dx) ` is equal to

A

`(y)/(x)`

B

`-(y)/(x)`

C

`(x)/(y)`

D

`-(x)/(y)`

Text Solution

Verified by Experts

The correct Answer is:
B
`xy=tan^(-1)(xy)+cot^(-1)(xy)=(pi)/(2)`
`implies xy=(pi)/(2)`
` :. x""(dy)/(dx)+y=0`
`implies (dy)/(dx)=(-y)/(x)`
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