Chapter 15 Section 15.6 Limits and Continuity; Equality of Mixed Partials.

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Chapter 15 Section 15.6 Limits and Continuity; Equality of Mixed Partials

Take derivative of z with respect to x twice. Take derivative of z first with respect to y then x. Take derivative of z first with respect to x then y. Take derivative of z with respect to y twice.

Equality of Mixed Partials At all points of continuity of the second derivative the mixed partials will be equal. This says it does not matter what order you take the higher derivatives in. This means take the derivative of this function 4 times, 3 of them treating x as the variable and one of them treating y as the variable.