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If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=...

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

A

-1

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Given , ` xe^(xy) = y + sin^(2) x `
On differentiating both sides w.r.t.x, we get ,
`therefore xe^(xy) [ x (dy)/(dx) + y] + e^(xy) = (dy)/(dx) + 2 sin x cos x `
`(x^(2) e^(xy) -1) (dy)/(dx) = sin 2x - e^(xy) - xye^(xy) `
` (dy)/(dx) = (sin 2x - e^(xy) - xye^(xy))/((x^(2) e^(xy)-1))`
` rArr (dy)/(dx_(x=0)) = (0 - e^(0) -0)/(x-1) = 1`
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