November 14th, 2011, 12:40 PM  #1 
Newbie Joined: Oct 2011 Posts: 14 Thanks: 0  differentiable function?
Let be a function on and when . Is differentiable at ? Is the differential of function is continuous at this point? Is this function differentiable at ? Can anyone give me a hand? 
November 14th, 2011, 01:37 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,394 Thanks: 545  Re: differentiable function? Quote:
For x = 1 and y near 0, f(x,y) ? 1/(2?y), which is not differentiable. For x and y near 0, f(x,y) ? {?(x/y)}/2  
November 17th, 2011, 09:22 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: differentiable function?
Mathman, "differentiable" is defined for functions of two variables, separately from the existance of the partial derivatives. It can be shown, however, that if a function is differentiable at a point, its partial derivatives must be continuous in a neighborhood of that point.


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