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May 5th, 2012, 05:09 PM  #1 
Senior Member Joined: Sep 2008 Posts: 105 Thanks: 0  Partials in Different Coordinates
Let and Show that and 
May 6th, 2012, 02:26 AM  #2 
Member Joined: Mar 2012 Posts: 60 Thanks: 0  Re: Partials in Different Coordinates
Chain rule in two variables Since you even ask, I suppose it is stated in your book Differentiating G with respect to r is the same as differentiating F with respect to r, where you must use the chain rule If this didn't help, just let me know and I will give you the solution 
May 6th, 2012, 08:55 AM  #3 
Senior Member Joined: Sep 2008 Posts: 105 Thanks: 0  Re: Partials in Different Coordinates
Thanks for answering. The section in my book is very small. I am getting confused because r depends on x, y and theta. I was trying to draw a schema to help, but I can't figure out how to do it.

May 6th, 2012, 11:47 AM  #4 
Member Joined: Mar 2012 Posts: 60 Thanks: 0  Re: Partials in Different Coordinates
You are actually just interested in how x and y depends on r, and those relationships you have already statet above df/dr = (df/dx)(dx/dr) + (df/dy)/(dy/dr) where I don't know how to make partial d:s 
May 6th, 2012, 11:59 AM  #5 
Senior Member Joined: Sep 2008 Posts: 105 Thanks: 0  Re: Partials in Different Coordinates
So then is dG/dr = dF/dr? Why?

May 6th, 2012, 12:24 PM  #6 
Member Joined: Mar 2012 Posts: 60 Thanks: 0  Re: Partials in Different Coordinates
Due to equality. Perform the same operation on two equal expressions and you must get the same result An example: 3+2=5 (3+2)/10 = 5/10 The equality still holds Differentiating both sides of an equation with respect to the same variable is no different really :P 
May 6th, 2012, 01:13 PM  #7 
Senior Member Joined: Sep 2008 Posts: 105 Thanks: 0  Re: Partials in Different Coordinates
I guess I didn't expect it to be that simple. Thanks for your help!

May 6th, 2012, 01:22 PM  #8 
Member Joined: Mar 2012 Posts: 60 Thanks: 0  Re: Partials in Different Coordinates
Haha, sometimes it's just too easy to see it Happy to help 

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coordinates, partials 
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