Question 383696
the curly d's mean partial derivative. essentially u differentiate your f, first with respect to x, and then to y. by that i mean, when u differentiate with respect to x, treat y as a constant, and then the other way arnd for dy

example: let f(x,y)=x^2 + y^2. then df/dx = 2*x + 0. the y^2 becomes 0 since we treat it as a constant. similarly df/dy = 0+2y. 
hope this helps