Partial Differentiation

By definition,the total differential for this function can be written as
du = f1 dx1 + f2dx2 +f3 dx3 +... +fn dxn



2012-05-09 08:46:54 補充：
<Example >
Consider function z = f(x,y)=xy²-2x²+3y.
The partial derivatives of x and y are
fx(x,y) = y² - 4x
fy(x,y) = 2xy + 3
, respectively. Therefore, the total differentiation of function z=f(x,y) is
dz = (y² - 4x)dx + (2xy + 3)dy

2012-05-22 10:53:31 補充：
If u = f(x, y, z),the total differential for this function can be written as
du = fx dx + fydy +fz dz