Differentiation Question 261
Question: If $ y=\frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}} $ , then $ \frac{dy}{dx}= $
[Roorkee 1971]
Options:
A) $ \frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}}[ \frac{3}{2}.\frac{1-\cos x}{1-\sin x}-\frac{1}{2x} ] $
B) $ \frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}}[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} ] $
C) $ \frac{2{{(x-\sin x)}^{1/2}}}{\sqrt{x}}[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} ] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \log y=\log 2+\frac{3}{2}\log (x-\sin x)-\frac{1}{2}\log x $
$ \Rightarrow \frac{dy}{dx}=y[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} ] $ .
BETA
