CPM Homework Help : CALC Problem 12-10

A particle moves along the curve $y =\operatorname{sin} x$ at a constant speed of $5$ units per second. Find $x^\prime(t)$ , the $x$ -component of the velocity vector, when $x = 2$ .

Hint:

$5=\sqrt{(x^\prime(t))^2+(y^\prime(t))^2}\text{ or }25=(x^\prime(t))^2+(y^\prime(t))^2$
$25=(x^\prime(t))^2+(x^\prime(t)\cos(x))^2)$
$x^\prime(t)=\sqrt{\frac{25}{1-\cos^2(x)}}$
Evaluate $x^\prime(2)$ .