arctan(sqrt(x^2-1)) derivative | What is derivative of arctan(sqrt(x^2-1)) or tan^-1(sqrt(x^2-1))?

Greetings dear friends. In this article, we will tell you how to take the derivative of the arctan(sqrt(x^2-1)) expression. We wish you good lessons...

$arctan(\sqrt{(x^2-1)})$ derivative

Let's take the derivative step by step:

👉 $\frac{d}{dx}tan^{-1}x=\frac{1}{1+x^2}$

👉 $\frac{d}{dx}arctan(\sqrt{(x^2-1)})=\frac{d}{dx}tan^{-1}(\sqrt{(x^2-1)})$

So we will first take the derivative of arctan. Then we take the derivative of the interior and multiply it.

So;

👉 $\frac{d}{dx}tan^{-1}(\sqrt{(x^2-1)})=\frac{1}{1+(\sqrt{(x^2-1)})^2}.\frac{1}{2.(\sqrt{(x^2-1)})}.2x$

👉 $\frac{x}{x^2.(\sqrt{(x^2-1)})}=\frac{1}{x.(\sqrt{(x^2-1)})}$

Answer : $\frac{1}{x.(\sqrt{(x^2-1)})}$