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

MCQ

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

A
${{y + 2\sin x} \over {2\sin y + x}}$
✓
${{y + \sin 2x} \over {2\sin y - x}}$
C
${{y + 2\sin x} \over {\sin y + x}}$
D
None of these

✓

Answer

Correct option: B.

${{y + \sin 2x} \over {2\sin y - x}}$

b
(b) ${\sin ^2}x + 2\cos y + xy = 0$

$ \Rightarrow 2\sin x\cos x - 2\sin y\frac{{dy}}{{dx}} + y + x\frac{{dy}}{{dx}} = 0$

$\therefore \frac{{dy}}{{dx}} = \frac{{y + \sin 2x}}{{2\sin y - x}}$.

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