v=e^(xy)=v(x,y)

Given the concrete form of the function f (), the following results can be derived: namely, transform f(u, v) into the function g(x, y) of x, y:

z = f(u，v) = f [u(x，y)，v(x，y)] = g(x，y)

Then calculate:

? z/？ x =？ g/？ x

? z/？ y =？ g/？ y

Since z is a function of (x, y), it is not dz/dx and dz/dy that need to be calculated, but the partial derivatives of z to x and y.

For example, suppose: f(u, v)=u+v //: that is, given a specific expression, it is easy to solve, and it is necessary to write a general expression.

More trouble!

u=x-y

v=e^(xy)

Then: z = f (u, v) = u+v = x-y+e (xy) = g (x, y)

So:? z/？ x=？ g/？ x= 1+ y e^(xy)

? z/？ y=？ g/？ y=- 1+x e^(xy)