Answer
$\pi \cos [\dfrac{\pi}{5}(x-4)]$
Work Step by Step
We have: $p(x)=2+5 \sin [\dfrac{\pi}{5}(x-4)]$
We differentiate both sides with respect to $x$.
$p^{\prime}(x)=\dfrac{d}{dx} [2+5 \sin [\dfrac{\pi}{5}(x-4)]] \\=0+5 \cos [\dfrac{\pi}{5}x-\dfrac{4\pi}{5}] \times \dfrac{\pi}{5}$
Simplify to obtain:
$p^{\prime}(x)=\pi \cos [\dfrac{\pi}{5}(x-4)]$
