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If sec((x^2-y^2)/(x^2+y^2))=e^a, then (d...

If `sec((x^2-y^2)/(x^2+y^2))=e^a,` then `(dy)/(dx)` is

A

`(y^(2))/(x^(2))`

B

`(y)/(x)`

C

`(x)/(y)`

D

`(x^(2)-y^(2))/(x^(2)+y^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `(x^(2)-y^(2))/(x^(2)+y^(2))=sec^(-1)(e^(a))`
Onn differentiating w.r.t. x, we get
`(x^(2)+y^(2)(2x-2y(dy)/(dx))=0-(x^(2)-y^(2))(2x+2y(dy)/(dx))=0`
`implies(x^(2)y+y^(3)+x^(2)y-y^(3))(dy)/(dx)`
`=(x^(3)+xy^(2)-x^(3)+xy^(2))`
`implies(dy)/(dx)=(y)/(x)`.
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