If ,(x + y) = 2xy, then y'(0) = - Vidyadip

MCQ

If $\ln \,(x + y) = 2xy,$ then $y'(0) =$

✓
$1$
B
$-1$
C
$2$
D
$0$

✓

Answer

Correct option: A.

$1$

a
(a) $\ln (x + y) = 2xy$

Differentiate both sides w.r.t $x,$

$\left( {\frac{1}{{x + y}}} \right)\,\left( {1 + \frac{{dy}}{{dx}}} \right) = 2\,\left( {x\frac{{dy}}{{dx}} + y} \right)$

==> $\frac{{dy}}{{dx}} = \frac{{1 - 2xy - 2{y^2}}}{{2{x^2} + 2xy - 1}}$

As at $x = 0,y = 1$, (From $\ln (x + y) = 2xy$)

Hence $y'(0) = \frac{{1 - 2}}{{ - 1}} = 1$.

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