Contextual Applications of Differentiation · Superchallenge problem

In $\triangle ABC$, side $a=7$ is increasing at $2$ units/s, side $b=5$ is decreasing at $1$ unit/s, and the included angle $C=60^\circ$ is increasing at $0.1$ rad/s. Using the Law of Cosines, $c^2=a^2+b^2-2ab\cos C$, find the rate of change of side $c$ at this moment, to three decimal places.