Unformatted text preview: singlevariable calculus, it is usually pretty easy to determine whether they exist and if so to calculate them formally. However, the existence of the partials is not by itself a guarantee that the function is diferentiable . ±or example, the function we considered in § 3.1 f ( x ) = b xy x 2 + y 2 if ( x,y ) n = (0 , 0) , at (0 , 0) has the constant value zero along both axes, so certainly its two partials at the origin exist and equal zero ∂f ∂x (0 , 0) = 0 ∂f ∂y (0 , 0) = 0...
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 Fall '08
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 Calculus, Derivative, constant value, equal zero, SingleVariable Calculus, essentially derivatives, origin exist

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