Differentiation Question 76
Question: If $ y=x[ ( \cos \frac{x}{2}+\sin \frac{x}{2} )( \cos \frac{x}{2}-\sin \frac{x}{2} )+\sin x ]+\frac{1}{2\sqrt{x}} $ , then $ \frac{dy}{dx}= $
Options:
A) $ (1+x)\cos x+(1-x)\sin x-\frac{1}{4x\sqrt{x}} $
B) $ (1-x)\cos x+(1+x)\sin x+\frac{1}{4x\sqrt{x}} $
C) $ (1+x)\cos x+(1+x)\sin x-\frac{1}{4x\sqrt{x}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=x[ ( \cos \frac{x}{2}+\sin \frac{x}{2} )( \cos \frac{x}{2}-\sin \frac{x}{2} )+\sin x ] $
$ +\frac{1}{2\sqrt{x}} $
Therefore $ y=x(\cos x+\sin x)+\frac{1}{2\sqrt{x}} $
Differentiating w.r.t. x, we have $ \frac{dy}{dx}=x\frac{d}{dx}(\cos x+\sin x)+(\cos x+\sin x)-\frac{1}{4}{x^{-3/2}} $
Therefore $ \frac{dy}{dx}=\frac{x[ -\frac{1}{2\sqrt{a^{2}-x^{2}}}(-2x) ]-(a-\sqrt{a^{2}-x^{2})}}{x^{2}} $ .
BETA
