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Product Rule

  1. Oct 23, 2005 #1
    How do I carry out the product rule for


    Is it possible to do the product rule with y'z' and after that multiply it by x?
  2. jcsd
  3. Oct 23, 2005 #2
    What variable is this respect to? Is it [tex]\frac{d}{dx},\frac{d}{dy}[/tex],etc.
  4. Oct 23, 2005 #3
    It's not respect to any variable. It's just three separate variable... for instance it can be xyz.... so i was thinking that i first do the product rule for yz which is y'z + z'y and then i use this result and multiply it by x and x'. I am not sure if I am allowed to do this.
  5. Oct 23, 2005 #4
    The product rule extends for three variables as follows. Let's say we have three functions that are in terms of x, we'll call them f(x),g(x), and h(x).

  6. Oct 23, 2005 #5
    Thank you, I really appreciate your help.
  7. Feb 10, 2008 #6
    I have a question regarding the product rule.

    Our modern physics textbook asks us to derive the following:

    [tex]d(\gamma mu)=m(1- \frac{u^2}{c^2})^{-3/2} du[/tex]

    Is it implied that this is with respect to u? I can see the chain rule here, but I'm not sure precisely how this differentiation is done.
  8. Feb 10, 2008 #7


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    Science Advisor

    First, please do not post a new question in someone else's thread. That is very rude- start your own thread.

    Second, strictly speaking, the right hand side is a differential with respect to u while the left side is just the differential of [itex]\gamma mu[/itex] and is not "with respect to" anything. If you were to rewrite it as
    [tex]\frac{d(\gamma mu)}{du}= m\left(1-\frac{u^2}{c^2}\right)^{-3/2}[/tex]
    then the derivative on the left is with respect to u.

    I can't tell you how to derive it since you haven't said what it is to be derived from- which, hopefully, you will do in a separate thread.
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