Answer
$$ h'(t)=-9\csc t \cot t+ \cot t -t \csc^2 t.$$
Work Step by Step
Since $ h(t)=9\csc t+t \cot t $, then, using the product rule: $(uv)'=u'v+uv’$ and also, using the facts that $(\csc x)'=-\csc x \cot x $ and $(\cot x)'=-\csc^2 x $, we have $$ h'(t)=(9\csc t)' +(t \cot t)'\\ =-9\csc t \cot t+ \cot t -t \csc^2 t.$$
