The derivative of sec(tan x) with respect to x is:

Question

The derivative of $\sec (\tan \sqrt{x})$ with respect to $x$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{s e c (t a n \sqrt{x}) t a n (t a n \sqrt{x}) s e c^{2} \sqrt{x}}{2 \sqrt{x}}$

Explanation:

Let $y = \sec (\tan \sqrt{x})$

So, $\frac{d y}{d x} = \frac{d [\sec (\tan \sqrt{x})]}{d (\tan \sqrt{x})} \times \frac{d (\tan \sqrt{x})}{d (\sqrt{x})} \times \frac{d (\sqrt{x})}{d x}$

$= \sec (\tan \sqrt{x}) \cdot \tan (\tan \sqrt{x}) \times \sec^{2} \sqrt{x} \times \frac{1}{2 \sqrt{x}}$

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

Solution

Q.
The derivative of $\sec (\tan \sqrt{x})$ with respect to $x$ is:

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

2 $\sec^{2} (\tan \sqrt{x})$

3 $\frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec^{2} \sqrt{x}}{x}$

4 $\sec^{2} (\tan x^{1 / 3})$

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Solution

Q. The derivative of sec(tanx) with respect to x is:

1 sec(tanx) tan(tanx) sec2x2x

2 sec2(tanx)

3 sec(tanx) tan(tanx) sec2xx

4 sec2(tanx1/3)