- #1
Liquid7800
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Homework Statement
Hello, recently in my calculus III class we went over some problems of the following form:
If 'for some given equation' show:
x(fx) +y(fxy) +fx= 0
For some examples I was playing around with the operations BEFORE I dived in and started solving for fx and fy and got the correct answers for some problems----so I thought Now is it possible to 're-arrange' the algebraic structure as such for the partial derivative operations?
x(fx) + y(fx(f+fy))=0 ; where 'f' is the undifferentiated function?
...in the same manner can you 'divide' out the partial derivative operations too? Therefore getting
Consider from the same equation above,
x(fx) = -(y)(fx)(f + fy)
We divide out fx
as we solve for 'x' getting:
x = -(y)(f + fy)
We then place 'x' back into the original equation and show that
-(y)(f + fy) = -(y)(f + fy)
Therefore to 'complete' the proof we just solve for fy and add it to f; where 'f' is the function; multiplied by 'y' and show that they do indeed equal 0. Thus allowing only to solve for fy to prove the problem?
Now re-arranging this problem algebraically may not make things any simpiler but sometimes it may AND it at least helps me see the big picture.
Is it possible to perform these kind of algebraic manipulations on these sort of 'proof' problems?
Thanks for your help as always