Chapter 4.3, Problem 39E

To determine

To find:The correct option.

Answer to Problem 39E

The correct option is A .

Explanation of Solution

Given Information: The function is $\frac{d}{dx}{\sec }^{-1}\left(x^2\right)$ .

Calculation:

The derivative of the function is,

  $\begin{array}{c}\frac{d}{dx}{\sec }^{-1}\left(x^2\right)=\frac{1}{\left|x^2\right|\sqrt{{\left(x^2\right)}^2-1}}\times \frac{d}{dx}\left(x^2\right)\left(\because \frac{d}{dx}{\sec }^{-1}\left(x\right)=\frac{1}{\left|x\right|\sqrt{x^2-1}}\right)\\ =\frac{1}{\left|x^2\right|\sqrt{{\left(x^2\right)}^2-1}}\times 2x\\ =\frac{2x}{\left|x^2\right|\sqrt{{\left(x^2\right)}^2-1}}\\ =\frac{2}{x\sqrt{x^4-1}}\end{array}$

Conclusion:

The correct option is A .