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If xe^(xy)-y=sin^(2)x then (dy)/(dx) at ...

If `xe^(xy)-y=sin^(2)x` then `(dy)/(dx)` at x = 0 is

A

0

B

1

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have `xe^(xy)-y=sin^(2)x`
When x = 0, y = 0
Differentiating w.r.t. x, we get
`1xxe^(xy)+x xx e^(xy)(y+xy')-y'=2 sin x cosx`
`therefore" "(dy)/(dx)=-((x.ye^(xy)+e^(xy)-2 sin x cos x)/(x^(2).e^(xy)-1))`
`rArr" "(dy)/(dx)_("(0,0)")=1`
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