Differentiation Question 242
Question: The derivative of $ \sqrt{\sqrt{x}+1} $ is
[SCRA 1996]
Options:
A) $ \frac{1}{\sqrt{x}(\sqrt{x}+1)} $
B) $ \frac{1}{\sqrt{x}\sqrt{x+1}} $
C) $ \frac{4}{\sqrt{x(\sqrt{x}+1)}} $
D) $ \frac{1}{4\sqrt{x(\sqrt{x}+1)}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ y=\sqrt{\sqrt{x}+1} $
$ \frac{dy}{dx}=\frac{1}{2\sqrt{\sqrt{x}+1}}\frac{d}{dx}(\sqrt{x}+1) $
$ \frac{dy}{dx}=\frac{1}{4\sqrt{x}.\sqrt{\sqrt{x}+1}}=\frac{1}{4\sqrt{x(\sqrt{x}+1)}} $ .
BETA
