1.

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)0A. 1B. `-1`C. 2D. `0`

Answer» Correct Answer - 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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