Answer
$-8.06$
Work Step by Step
We have: $v=3e^2 +5g^3$
Now, at $v=200$ and $g=3.0$, we have: $200=3e^2+135 \implies e=4.65$
We need to differentiate both sides with respect to $x$.
$\dfrac{dv}{dg}=3.2e \dfrac{de}{dg}+5.3g^2 \dfrac{dg}{dg} \\ \dfrac{de}{dg}=\dfrac{-15 g^2}{6e}$
Plug the values in the given equation to obtain:
$ \dfrac{de}{dg}=\dfrac{-225}{27.9}=-8.06$
