Differentiation Question 296
Question: If $ y=\sqrt{\sin x+y}, $ then $ \frac{dy}{dx} $ equals to
[RPET 2001]
Options:
A) $ \frac{\sin x}{2y-1} $
B) $ \frac{\cos x}{2y-1} $
C) $ \frac{\sin x}{2y+1} $
D) $ \frac{\cos x}{2y+1} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=\sqrt{\sin x+y}, $
Therefore $ y^{2}=\sin x+y $
Differentiate with respect to x, $ 2y.\frac{dy}{dx}=\cos x+\frac{dy}{dx} $
Therefore $ \frac{dy}{dx}(2y-1)=\cos x $
Therefore $ \frac{dy}{dx}=\frac{\cos x}{2y-1} $ .
BETA
