Differentiation Question 231
Question: $ \frac{d}{dx}\sqrt{x\sin x}= $
[AISSE 1985]
Options:
A) $ \frac{\sin x+x\cos x}{2\sqrt{x\sin x}} $
B) $ \frac{\sin x+x\cos x}{\sqrt{x\sin x}} $
C) $ \frac{x\sin x+\cos x}{\sqrt{2\sin x}} $
D) $ \frac{\sin x+x\cos x}{2\sqrt{x\sin x}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y^{2}=x\sin x\Rightarrow 2y\frac{dy}{dx}=\sin x+x\cos x $
$ \therefore \frac{dy}{dx}=\frac{[\sin x+x\cos x]}{2\sqrt{x\sin x}} $ .
BETA
