MCQ
The derivative of $\sqrt {\sqrt x + 1} $ is
  • A
    ${1 \over {\sqrt x (\sqrt x + 1)}}$
  • B
    ${1 \over {\sqrt x \sqrt {x + 1} }}$
  • C
    ${4 \over {\sqrt {x(\sqrt x + 1)} }}$
  • ${1 \over {4\sqrt {x(\sqrt x + 1)} }}$

Answer

Correct option: D.
${1 \over {4\sqrt {x(\sqrt x + 1)} }}$
d
(d) $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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