Answer
$$s'=\frac{4}{\pi}(\cos3t-\sin5t)$$
Work Step by Step
$$s=\frac{4}{3\pi}\sin 3t+\frac{4}{5\pi}\cos5t$$
The derivative of function $s$ is: $$s'=\frac{4}{3\pi}(\sin 3t)'+\frac{4}{5\pi}(\cos5t)'=\frac{4}{3\pi}\cos 3t(3t)'+\frac{4}{5\pi}(-\sin5t)(5t)'$$
$$s'=\frac{4}{3\pi}\cos 3t\times3-\frac{4}{5\pi}\sin5t\times5=\frac{4}{\pi}\cos 3t-\frac{4}{\pi}\sin5t$$
$$s'=\frac{4}{\pi}(\cos3t-\sin5t)$$
