November 14th, 2011, 11:40 AM  #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, 12:37 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,494 Thanks: 578  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, 08:22 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.


Tags 
differentiable, function 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
where the function is differentiable?  alexmath  Calculus  5  June 12th, 2013 01:20 AM 
differentiable function  Camille91  Real Analysis  1  October 31st, 2011 02:09 PM 
not differentiable function  munkaka  Real Analysis  7  April 29th, 2011 01:21 AM 
no differentiable function.....  rose3  Real Analysis  1  January 14th, 2010 04:50 AM 
differentiable function  babyRudin  Real Analysis  5  November 8th, 2008 03:50 AM 