April 5th, 2009, 02:11 PM  #1 
Newbie Joined: Apr 2009 Posts: 2 Thanks: 0  Quick question
I am working on something for my dissertation and I need to know if I can establish any relationship/bound on the difference between a cross derivative and the product of partial derivatives, that is, d2f/dxdy (=,<,>?) df/dx*df/dy (Any reference?) This must be superobvious, but I thought that the asking was going to be the mos efficient way of finding out. Thanks, DD 
April 5th, 2009, 03:15 PM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Quick question
In general, we can't say anything about any relationship. Note that, dimensionally speaking, where defines the dimensions of a term whereas so we wouldn't expect any meaningful identity between the two. One relationship that does involve the two different derivatives is 
April 5th, 2009, 04:40 PM  #3  
Newbie Joined: Apr 2009 Posts: 2 Thanks: 0  Re: Quick question Quote:
This is great thanks very much. If you don't mind I am going to ask something else related to what you replied. The function f I am working with is between [0,1], can't that help me saying that d2f/dxdy>df/dx*df/dy? (from your answer this seems to be a correct statement, but I am not sure) Thanks once again for your reply  
April 8th, 2009, 08:44 AM  #4  
Senior Member Joined: Apr 2009 From: Mesa, Arizona Posts: 161 Thanks: 0  Re: Quick question Quote:
(h*g)' = h'g +g'h for a strong "central" domain in R. lim (h(x +h)g(x + h)  h(x)g(x))/h must be consider when x is not a point due to the nature of the topology need in the usage of limits. h is a variable representing "a moving number." Kind of like a vibrational slope, "its vibrates at a singularity."  

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