My textbook (nonlinear dynamics and chaos, strogatz), uses Green's theorem at some point (the actual use is not relevant for my question I hope):
given a real valued function $g(\vec x)$ such that $\nabla\cdot (g\dot x)$ [...] then using Green's theorem, $$\int\int_A\nabla\cdot(g\dot {\vec x})dA=\int_Cg\dot {\vec x }\cdot n dl $$ where
What does $g\dot {\vec x}$ mean here? $g$ is a function, so why isn't it written $g(\dot {\vec x})$? There must be a difference between the meaning of these two notations.