Partial Derivatives & the Gradient · Challenge problem

A triangle has sides $a = 3$ and $b = 5$ with included angle $C = \dfrac{2\pi}{3}$, so its third side is $c = 7$ by the law of cosines. If $a$ and $b$ are held fixed, find the rate $\dfrac{\partial c}{\partial C}$ at which the third side changes with the angle.