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Directional Derivatives


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:

 

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