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