means "the derivative of uwith respect to arc lengthalong the direction [itex]\theta[/itex]".

For example, suppose the path is just the straight line y= x. It's length, between and is, of course, . That is, and .

If , Then, along the path y= x, . It's derivative is .

Of course, with y= x as the path, and with u(x,y)= x^2+ 2y, we have and [tex]\frac{\partial u}{\partial y}= 2.

which, because is the same as .