$\backslash$table$[[x,-1,0,2,3],[g(x),4,1,0,-2],[g^{\text{'}}(x),-2,-6,-3,-4]]$

The table above gives selected values for a differentiable and decreasing function $g$ and its derivative. Let $f$ be the function with $f(3)=2$ and derivative given by $f^{\text{'}}(x)=xcos(e^{\text{'}}).$

$($a$)$ Find $f^{\text{'}\text{'}}($sin $2).$ Express your answer as a decimal appraximation.

Note On your AP Exam, you will handwrite your responses to free$-$responsequestions in a test booklet

$($b$)$ Let $h$ be the function defined by $h(x)=g(f(2x)).$ Find $h^{\text{'}}(1\mathrm{.}5).$ Express your answer as a decimal approximation.

$($c$)$ Write an equation for the line tangent to the graph of $g^{-1},$ the inverse function of $g$ at $x=-2.$