Differentiation Question 2
Question: If $ \cos (x+y)=y\sin x, $ then $ \frac{dy}{dx}= $
[AI CBSE 1979]
Options:
A) $ -\frac{\sin (x+y)+y\cos x}{\sin x+\sin (x+y)} $
B) $ \frac{\sin (x+y)+y\cos x}{\sin x+\sin (x+y)} $
C) $ -\frac{\sin (x-y)+y\cos x}{\sin x+\sin (x-y)} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \cos (x+y)=(y\sin x) $
Therefore $ -\sin (x+y)( 1+\frac{dy}{dx} )=y\cos x+\sin x\frac{dy}{dx} $
Therefore $ \frac{dy}{dx}=-\frac{y\cos x+\sin (x+y)}{\sin (x+y)+\sin x} $ .
BETA
