Answer
$h(t)=-4\pi\csc^2{(\pi t+2)}\cot{(\pi t +2)}.$
Work Step by Step
$u=\cot{(\pi t+2)}$; $\dfrac{du}{dt}=-\pi\csc^2{(\pi t+2)}$
$h(u)=2u^2;\dfrac{d}{du}h(u)=4u$
$\dfrac{d}{dt}h(t)=\dfrac{d}{du}h(u)\times\dfrac{du}{dt}=(-\pi\csc^2{(\pi t+2)})(4\cot{(\pi t +2)})$
$=-4\pi\csc^2{(\pi t+2)}\cot{(\pi t +2)}.$
