Answer
$$f_x= 2,f_y= 2y.$$
Work Step by Step
To calculate the partial derivatives, treat all variables as constant except the variable we are deriving with respect to.
Since $f(x,y)=2x+y^2$, then we have
$$f_x=\frac{\partial f}{\partial x}=2,$$
$$f_y=\frac{\partial f}{\partial y}=2y.$$
