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If y is a function of xa n dlog(x+y)-2x ...

If `y` is a function of `xa n dlog(x+y)-2x y=0,` then the value of `y^(prime)(0)` is (b) `-1` (c) 2 (d) 0

A

1

B

`-1`

C

2

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that, ` log(x+y) = 2xy` ..(i)
` :. " At " x = 0, rArr log (y) =0rArr y = 1`
` :. ` To find ` (dy)/(dx) ` at (0, 1)
On differentiating Eq. (i) w.r.t. X, we get
`1/(x+y) (1+(dy)/(dy))= 2x (dy)/(dx) + 2y* 1`
` rArr" " (dy)/(dx) = (2y(x+y)-1)/(1-2(x+y)x) `
` rArr" " ((dy)/(dx))_("(0,1)") = 1`
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