Q. Differential coefficient of $\sqrt{\sec\sqrt{x}\ }\$is
A) $\frac{1}{4\sqrt{x}}\sec\sqrt{x}\sin\sqrt{x}$
B) $\frac{1}{4\sqrt{x}}\left( \sec\sqrt{x} \right)^{3/2}.\sin\sqrt{x}$
C) $\frac{1}{2}\sqrt{x}\ \sec\sqrt{x}\ \sin\sqrt{x}$
D) $\frac{1}{2}\sqrt{x}\left( \sec\sqrt{x} \right)^{3/2}.\sin\sqrt{x}$
Explanation
(b)
Let $y = \sqrt{\sec\sqrt{x}}$
$\Rightarrow \ \ \frac{dy}{dx}\ = \ \frac{1}{2\sqrt{\sec\sqrt{x}}}.\sec{\sqrt{x}.\tan{\sqrt{x}.\frac{1}{2\sqrt{x}}}}$
$= \frac{1}{4\sqrt{x}}{(\sec{\sqrt{x})}}^{3/2}.\sin x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.