Given a polynomial, say p(x, y) = 3x^2y + x + 2y + 1, we can differentiate it by a variable, say x and get \partial p(x, y) / \partial x = 6xy + 1.
We can also differentiate it by both of its variable and get the vector [6xy+1, 3x^2+1].
differentiate
Given a polynomial, say p(x, y) = 3x^2y + x + 2y + 1, we can antidifferentiate it by a variable, say x and get \int_0^x p(X, y)\mathrm{d}X = x^3y + 1/2x^2 + 2xy + x.
We can also antidifferentiate it by both of its variable and get the vector [x^3y + 1/2x^2 + 2xy + x, 3/2x^2y^2 + xy + y^2 + y].
antidifferentiate