Integrate Over XY Plane for Simplest Partial Derivatives

[coverband]

which will yield the simplest partial derivatives
i.e. integrate over the xy plane if dz/dx and dz/dy yield the simplest expression?

 

[Defennder]

I don't understand your question. What function (be it scalar or vector) are you integrating over and how is it expressed?

 

[HallsofIvy]

Are you talking specifically about finding the area of a surface? Just integrating a function over a surface doesn't necessarily have anything to do with the derivatives.

Basically, you just have to be sure that the surface projects one-to-one onto the plane you are using. As long as the surface is given by the function z= f(x,y), you can be sure the xy-plane will work. If the surface is given by x= f(y,z) or y= f(x,z) then the yz-plane and xz-plane, respectively will work. More generally, if you can write the surface with parametric equations, x= f(u,v), y= g(u,v), z= h(u,v) with f, g, and h functions, then you can integrate over the "uv-plane". If z= f(x,y), then x= x, y= y, z= f(x,y) are parametric equations with "parameters" x and y.