Total Differential

Consider the function, u(x, y, z) then its total differential is defined:

In here, the dx, dy, dz, is a tiny quantity on each axis, x, y, z, and the

is the rates of change of u(x, y, z) that it is caused by the tiny change of x, and

is the rates of change of u(x, y, z) that it is caused by the tiny change of y, and

is the rates of change of u(x, y, z) that it is caused by the tiny change of z.
Therefore, thecan be explained that it is a tiny quantity of change of u(x, y, z) by tiny change of x, andis a tiny quantity of change by tiny change of y, andis a tiny quantity of change by tiny change of z.
So the total differential du is equal to change of direction x and change of direction y and change of direction z.