The integral constant c should be added to the indefinite integral result of univariate function, and the function ψ (y) of y should be added after the original function of bivariate function is integrated with x.

For example:

Find the derivative of x: 2x+2zz' x = e z+xe z' x = > x = > z' x = (2x-e z)/(xe z-2z)

Find the derivative of y: 2y+2z z 'y = xe z 'y = > y = > z 'y = 2y/(xe z-2z)

dz = z ' x dx+z ' y dy =(2x-e^z)/(xe^z-2z)dx+2y/(xe^z-2z)dy

Essence:

The essence of multivariate function is a relationship, which is a definite correspondence between two sets. The elements of these two sets can be numbers; It can also be a point, a line, a surface or a body; It also includes vectors, matrices, etc. The result corresponding to one or more elements can be a unique element, that is, a single value. It can also be multiple elements, that is, multiple values.