Product rule - differentiation

Discussion in 'Math' started by amilton542, Feb 2, 2012.

  1. amilton542

    Thread Starter Active Member

    Nov 13, 2010
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    Let's say you've got a product of n different functions, as many as you want it doesn't matter (but not two), I'll choose 5 for simplicity. If I wanted to calculate dy/dx, could I use this method?

    (uvwxz)'= u'vwxz + uv'wxz + uvw'xz + uvwx'z + uvwxz'
     
    Last edited: Feb 2, 2012
  2. Zazoo

    Member

    Jul 27, 2011
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    Yes, that works.
     
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  3. Georacer

    Moderator

    Nov 25, 2009
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    Are the rest of the functions related to x?

    What you wrote is the derivative of the product. Do you want dy/dx instead?
     
  4. amilton542

    Thread Starter Active Member

    Nov 13, 2010
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    Yes I wanted the derivative of the product.

    I introduced all the new y values and subtracted the old ones to give me the difference in y, then I took the limit when Δx tends to zero, then put it in that notation for a clear visual inspecton.

    Please excuse my terminology, I thought dy/dx was the total rate of instantaneous change e.g. the derivative which can alse be written as (uvwxz)'. Is that correct?
     
    Last edited: Feb 2, 2012
  5. amilton542

    Thread Starter Active Member

    Nov 13, 2010
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    Ohhhh rats! I've made an error in the alphabet! How embarrassing. I've used y as notation in the functions, sorry folks!
     
    Last edited: Feb 2, 2012
  6. Zazoo

    Member

    Jul 27, 2011
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    As Georacer pointed out, the assumption here is that u, v, w and z are all functions of x themselves (and not separate variables.)
     
  7. amilton542

    Thread Starter Active Member

    Nov 13, 2010
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    When did I say they were seperate variables? An increment in x will cause incremental changes in all functions.
     
  8. Zazoo

    Member

    Jul 27, 2011
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    You didn't, I was just pointing out that my answer was based on that assumption.
     
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