Answer
$p^{\prime}(x)=\dfrac{\pi}{2} \sin [\dfrac{\pi}{6}(x+3)]$
Work Step by Step
We have: $p(x)=10-3 \cos [\dfrac{\pi}{6}(x+3)]$
We differentiate both sides with respect to $x$.
$p^{\prime}(x)=\dfrac{d}{dx} [10-3 \cos [\dfrac{\pi}{6}(x+3)]] \\=0-3 \times -\sin [\dfrac{\pi}{6}(x+3)] \times \dfrac{\pi}{6}$
Simplify to obtain:
$p^{\prime}(x)=\dfrac{\pi}{2} \sin [\dfrac{\pi}{6}(x+3)]$
