I was working on problem #2 of problem set 4 part b, where you are supposed to find the angle of intersection of 2 surfaces at a particular point. f(x,y)=x^2-y^2; g(x,y)=2+(x-y)^2. point is (2,1,3). I understand that to do this, I need to find the partial derivatives for the 2 surfaces at that point for each function, and then find the normal to each of the tangent planes. The answer key does this, but it states to find the normal for the first plane, they use N1=(Fx(2,1), Fy(2,1), -1). Where Fx is derivative w/ respect to x; where does this formula come from?

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THANK YOU!! Totally makes sense now! : )

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