Question

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

• A. $\frac{1}{4\sqrt{x}}sec\sqrt{x}\,sin\sqrt{x}$
• B. $\frac{1}{4\sqrt{x}}\left(sec\sqrt{x}\right)^{3/2}\cdot sin\sqrt{x}$
• C. $\frac{1}{2}\sqrt{x}sec\sqrt{x}sin\sqrt{x}$
• D. $\frac{1}{2}\sqrt{x}\left(sec\sqrt{x}\right)^{3/2}\cdot sin\sqrt{x}$

Answer 1

Answer: (B)

Let $y=\sqrt{sec\sqrt{x}}$
Differentiating $w$.$r$.$t$. $x$, we get
$\frac{dy}{dx}=\frac{1}{2\sqrt{sec\sqrt{x}}}\cdot sec\sqrt{x}\cdot tan\sqrt{x}\cdot\frac{1}{2\sqrt{x}}$
$=\frac{1}{4\sqrt{x}}\left(sec\sqrt{x}\right)^{1/2} \frac{sin\sqrt{x}}{cos\sqrt{x}}$
$=\frac{1}{4\sqrt{x}}\left(sec\sqrt{x}\right)^{3/2}\cdot sin\sqrt{x}$