Definition: The derivative of f at P0(x0, y0)
in the direction of the unit vector u = u1i + u2j is
denoted by Duf(x0, y0) and is the number
provided this limit exists. The definition for functions of three variables is entirely similar.
Example: Find the derivative of f(x, y) = x2 + xy at P0(1,
2) in the direction 
.
Evaluate f along the line through P0 in the direction u:
Differentiate with respect to the
parameter:
Evaluate:
