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Homework Help: Extended product rule for derivatives

  1. Nov 22, 2008 #1
    Can someone please explain it to me? My handwriting wasn't at its best when I was taking notes in class and now I can't read it. The teacher showed an example that I jotted down but what's the general rule?
  2. jcsd
  3. Nov 22, 2008 #2
    Maybe you should consult your textbook or take notes more carefully.
    The usual product rule for differentiation reads
    where u,v are functions.

    What do you mean by extended product rule?
  4. Nov 22, 2008 #3
    I meant if you have 3 or more terms, like y = sinxcosxlnx and you want the derivative.
  5. Nov 22, 2008 #4


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    For three terms: (uvw)'=(uv)'w+(uv)w'=u'vw+uv'w+uvw'.

    As you can see, this can be extended to 4 terms and beyond quite readily.
  6. Nov 22, 2008 #5


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    It's easy to derive yourself, using the regular problem rule. If you have y = f(x)g(x)h(x), then use the formula Pete Callahan posted, using u=f(x), v=(g)h(x).
    So then y' = uv' + vu'
    Then use the product rule again to find v'
  7. Nov 22, 2008 #6
    Thanks everyone. This makes more sense now.
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