If (x + y) = y x, then dy dx = - Vidyadip

MCQ

If $\cos (x + y) = y\sin x,$ then ${{dy} \over {dx}} = $

✓
$ - {{\sin (x + y) + y\cos x} \over {\sin x + \sin (x + y)}}$
B
${{\sin (x + y) + y\cos x} \over {\sin x + \sin (x + y)}}$
C
$\frac{{y\cos x - \sin (x + y)}}{{\sin x - \sin (x + y)}}$
D
None of these

✓

Answer

Correct option: A.

$ - {{\sin (x + y) + y\cos x} \over {\sin x + \sin (x + y)}}$

a
(a) $\cos (x + y) = (y\sin x)$

==> $ - \sin (x + y)\left( {1 + \frac{{dy}}{{dx}}} \right) = y\cos x + \sin x\frac{{dy}}{{dx}}$

==> $\frac{{dy}}{{dx}} = - \frac{{y\cos x + \sin (x + y)}}{{\sin (x + y) + \sin x}}$.

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