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Unformatted text preview: x , etc.) 3 Second Order Partial Derivatives f xx = f yy = f xy = f yx = Example 1 f ( x, y ) = cos( xy ) Note: f xy = f yx for functions such that f xx , f yy , f xy , and f yx all exist and are continuous. 4 Example 2 z = 1x + y3 x 2 y Theorem. Diﬀerentiability of f ( x, y ) If the partial derivatives f x and f y exist near ( a, b ) and are continuous at ( a, b ), then f is diﬀerentiable at ( a, b ). Geometric Interpretation f xx = f yy = f xy = f yx = 5...
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 Spring '03
 MECothren
 Derivative, Multivariable Calculus, fxy, fyx, fyy, Defn. Partial Derivative

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