Multivariable Calculus | Differentiability

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We give the definition of differentiability for a multivariable function and provide a few examples.

  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. calculus
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Комментарии
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Beautiful use of the gradient and the dot product! Woo hoo! Great! Don't stop, Michael!!!! :-)

ezrasteinberg
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Omg I'm so grateful!! You're really the best !!

nailabenali
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WHY has the criteria of differentiability already assumed f is differentiable by writing fx and fy? Is that not circular logic?

keithchan
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Great example. At min 8, 43 the limit is 0, ok, but it should be (x-2), right? Thanks

henriquenunes
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back at it again with them early uploads!

CDChester
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To check that the function is differentiable at a given point, isn't it enough to check that partial derivatives are defined at the given point? For example in the first example partial with respect to x is 4x and with respect to y is -4, both of which are well defined at (2, -3). Would that be a good proof?

backyard
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he cancelled the - 4y with the other - 4y in the video but they do not have opposite signs.

michaelempeigne