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Homework Help: Partial Derivatives, and Differentiable

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    I want to show that the partials exist for a certain function.

    2. Relevant equations

    My book says that if a function f is differentiable at a point x then the partial derivatives exist.

    3. The attempt at a solution

    Rather than showing f is differentiable, I am curious if it is sufficient to just use the limit definition of a partial derivative and show that the limit exists?

    Thank you for your time.
  2. jcsd
  3. Jan 29, 2012 #2


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    Yes, to show the partials exists just use the limit definition. A function can fail to be differentiable and still have the partials exist.
  4. Jan 29, 2012 #3
    Thank you for the help.
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