Question

Find the derivative of $\sqrt{\tan x}$ with respect to $x$ using the first principle.

• A. $\frac{se{c}^{2}x}{2\sqrt{tanx}}$
• B. $\frac{secx}{2\sqrt{tanx}}$
• C. $\frac{se{c}^{2}x}{\sqrt{tanx}}$
• D. $\frac{se{c}^{2}x}{2\sqrt{tan}}$

Answer 1

The correct option is A $\frac{se{c}^{2}x}{2\sqrt{tanx}}$

$y=\sqrt{\tan x}$

$\Rightarrow \frac{dy}{dx}=\frac{1}{2\sqrt{\tan x}}\times {\sec }^{2}x$

$=\frac{{\sec }^{2}x}{2\sqrt{\tan x}}$

Hence, the answer is $\frac{{\sec }^{2}x}{2\sqrt{\tan x}}.$