(Faster than light) The derivative of … in Example 9 is

These problems resolve the speed of light paradox in Example 9.

(Faster than light) The derivative of $y=100\tan \theta$ in Example 9 is $y^{\prime }=100{\sec }^2\theta {\theta }^{\prime }=200\pi {\sec }^2\theta$. Therefore $y^{\prime }$ passes $c$ (the speed of light) when ${\sec }^2\theta$ passes ____. Such a speed is impossible—we forget that light takes time to reach $B$.

This exercise builds on another exercise in its source book, which isn't shown here.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §4.2 Implicit Differentiation and Related Rates, #17