# Chap3 - b Derivative of a single variable function)lim x df...

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Unformatted text preview: b Derivative of a single variable function: ( ) () '()lim x df fx x fx fx dx x Ξβ +Ξ β = β‘ Ξ erivatives of a twoariable function: Chapter 3: Multivariate Calculus βOnly the Basics b Derivatives of a two-variable function: (,) ( ,) (,) lim (,) (,) (, ) (,) lim (,) x x y y fxy fx xy fxy fxy x x fxy fxy y fxy fx y y y Ξβ Ξβ β +Ξ β β‘ = β Ξ β +Ξ β β‘ = β Ξ Higher order derivatives b Second derivatives of f(x,y) in x-and y-directions: 2 2 2 2 ( ,) (,) lim (,) (, ) (,) lim (,) x x xx x y x yy y fx xy fxy f f fx y x x x x fxy y fxy f f fx y y y y y Ξβ Ξβ +Ξ β β ββ = β‘ = β β β Ξ +Ξ β β ββ = β‘ = β β β Ξ b Mixed derivative: (,) ( ,) (,) lim (,) (,) (, ) (,) lim (,) y y y xy x x x x yx y fxy fx xy fxy f fx y x x y x fxy fxy y fxy f fx y y y x y Ξβ Ξβ β +Ξ β ββ = β‘ = β β β Ξ β +Ξ β ββ = β‘ = β β β Ξ b...
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• Spring '08
• Staff
• lagrange multipliers, A Single, Disprosio, Three-dimensional Integrals, lim βx, Two-dimensional Integrals

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Chap3 - b Derivative of a single variable function)lim x df...

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