(Solved): CThe manufacturing process for Widgets ( \( w \) ) requires first turning Goop \( (\mathrm{g}) \) i ...

CThe manufacturing process for Widgets ( \( w \) ) requires first turning Goop \( (\mathrm{g}) \) into Sludge (s), then turning Sludge into Widgets, according to the following production functions: \[ \begin{array}{l} s(g)=3 g+0.1 g^{2} \\ w(s)=4 s-0.01 s^{2} \end{array} \] Find \( \frac{d w}{d g} \) when \( g=10 \)