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) \[\frac{1}{4\sqrt{x(\sqrt{x}+1)}}\]
Correct Answer: D
Solution :
\[y=\sqrt{\sqrt{x}+1}\] \[\frac{dy}{dx}=\frac{1}{2\sqrt{\sqrt{x}+1}}\frac{d}{dx}(\sqrt{x}+1)\] \[\frac{dy}{dx}=\frac{1}{4\sqrt{x}.\sqrt{\sqrt{x}+1}}=\frac{1}{4\sqrt{x(\sqrt{x}+1)}}\].
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