Differential coefficient of x is - Vidyadip

MCQ

Differential coefficient of $\sqrt {\sec \sqrt x } $ is

✓
${1 \over {4\sqrt x }}{(\sec \sqrt x )^{3/2}}\sin \sqrt x $
B
${1 \over {4\sqrt x }}\sec \sqrt x \sin \sqrt x $
C
${1 \over 2}\sqrt x {(\sec \sqrt x )^{3/2}}\sin \sqrt x $
D
${1 \over 2}\sqrt x \sec \sqrt x \sin \sqrt x $

✓

Answer

Correct option: A.

${1 \over {4\sqrt x }}{(\sec \sqrt x )^{3/2}}\sin \sqrt x $

a
(a) $\frac{d}{{dx}}\left( {\sqrt {\sec \sqrt x } } \right) = \frac{1}{{2\sqrt {\sec \sqrt x } }}.\frac{d}{{dx}}(\sec \sqrt x )$

$ = \frac{1}{{2{{(\sec \sqrt x )}^{1/2}}}}.\sec \sqrt x .\tan \sqrt x .\frac{1}{{2\sqrt x }}$

$=\frac{1}{4\sqrt{x}}.{{(\sec \sqrt{x})}^{1/2}}.\frac{\sec \sqrt{x}}{\cos \sqrt{x}} $

$=\frac{1}{4\sqrt{x}}{{(\sec \sqrt{x})}^{3/2}}.\sec \sqrt{x}$

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