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Parials and Derivatives

  1. Feb 11, 2009 #1
    Is it possible to have a function that has bounded paritial derivatives, but is not differential? Can you give me an example? And if possible explain how this is possible?

    I am having trouble understanding this calculus concept. Thanks.
     
  2. jcsd
  3. Feb 12, 2009 #2

    CompuChip

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    I assume that you meant "differentiable" instead of "differential"?

    How about f(x) = |x|.
    For all x, [tex]|f'(x)| \le 1[/tex]
    however, f(x) is not differentiable.

    The boundedness of partial derivatives and differentiability don't have much to do with each other. On the other hand, for example, the derivative of f(x) = x2 is unbounded although f(x) is perfectly well differentiable (infinitely often, even).
     
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