If x e^ xy = y + ^2 x, then at x = 0, dy dx = - Vidyadip

MCQ

If $x{e^{xy}} = y + {\sin ^2}x$, then at $x = 0,{{dy} \over {dx}} = $

A
$-1$
B
$-2$
✓
$1$
D
$2$

✓

Answer

Correct option: C.

$1$

c
(c) We are given that $x{e^{xy}} = y + {\sin ^2}x$

When $x = 0$, we get $y = 0$

Differentiating both sides with respect to $x$, we get

${e^{xy}} + x{e^{xy}}\left[ {x\frac{{dy}}{{dx}} + y} \right] = \frac{{dy}}{{dx}} + 2\sin x\cos x$

Putting $x = 0,\,y = 0$, we get $\frac{{dy}}{{dx}} = 1$.

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