Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 611: 20

$$\sqrt{2}$$

Since speed is given by \begin{align*} \frac{d s}{d t}&=\sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}}\\ &=\sqrt{ \frac{1}{1-t^2}+\frac{1}{(1+t^2)^2}} \end{align*} Then \begin{align*} \frac{d s}{d t}\bigg|_{t=0} &=\sqrt{1+1} \\ &=\sqrt{2} \end{align*}