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A quotation then a question

  1. Mar 10, 2009 #1
    "
    (dy/dx) = (dy/du)(du/dx)

    Caution: Notice that if (dy/du) and (du/dx) were quotients rather than expressions for derivatives, we could cancel the du`s and make (5) into an identity. But we stree that du has not been defined as an entity, and consequently it is not legitimate to cancel the du`s. Nonetheless, the resemblance between (5) and an algebraic identity makes it easy to remember.
    "

    so, he`s saying that I can`t cancel out the du`s, because they are not quotients, but expressions for derivative..
    but I think that they can be canceled out!? is that true?
    and yes they are expressions for derivative, but also they are quotients..
    and I understand that we need them, and it would be meaningless to cancel them..
    its just that I think he`s giving me wrong information when he said that I "can`t cancel them out" because "they are expressions for derivatives"

    Am I wrong?
     
  2. jcsd
  3. Mar 10, 2009 #2
    That's the chain rule. It is a legitimate identity, but it is not quite as immediately obvious as some may think.
     
  4. Mar 10, 2009 #3

    matt grime

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    You should not think of them as quotients.

    The derivative dy/dx is the limit of quotients. That is *not* the same thing as being a quotient. In some cases identities can be remembered because things cancel as if it were legitimate to separate the dy and dx. You should *not* think that you can separate them out at this stage.
     
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