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 Post subject: proving differentiability of a multivariable functionPosted: Sun, 3 Jun 2012 05:48:32 UTC
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Joined: Wed, 30 Nov 2011 23:20:57 UTC
Posts: 45
This proof, again, is very intuitive, but is not obvious if done mathematically.
Prove: that if is differentiable at x, then all the first partials exist at x and (x) = (x)i + (x)j + (x)k.
Thank you for any responses.

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 Post subject: Re: proving differentiability of a multivariable functionPosted: Sun, 3 Jun 2012 06:30:33 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
jpritch422 wrote:
This proof, again, is very intuitive, but is not obvious if done mathematically.
Prove: that if is differentiable at x, then all the first partials exist at x and (x) = (x)i + (x)j + (x)k.
Thank you for any responses.

What have you tried? This is essentially the definition of the derivative.

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