I have been doing an exercise problem in Multivariable calculus, namely I used Green's theorem. But there is something in the solution that I do not fully understand.
1)(Marked by the red rectangle): How did they get that $f_x(x,y)$ is equal to the specified, they didn't use any chain rule in order to calculate the derivative of $f(x,y)$?
2)Also, after that they wrote: "On $C$ we have $f_x(x,y)=g'(2)x/2=x/2$". Didn't they calculate $f_{xx}$ here, and not $f_x$?
