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Stuck getting derivative when can't isolate my variable

  1. Feb 28, 2015 #1
    Hi. This is not a homework assignment. I am working to get an extrema on a graph that involves a bunch of functions and got stuck on one step:

    How to get the derivative of:
    [tex]\frac{dy}{dn} = \frac{nc(a+b)}{nc+a}[/tex]

    I can't get "n" in a place where I recognize how to get the derivative of it. I get stuck here after the first step..
    [tex] nc(a+b)*(nc+a)^{-1}[/tex]

    or do I use the quotient rule where it ends up:
    [tex] \frac{[nc(a+b)]'*(nc+a) - nc(a+b)(nc+a)'}{(nc+a)^2} [/tex]
    [tex] \frac{c(a+b)*(nc+a) - nc(a+b)(c)}{(nc+a)^2} [/tex] ??

    Can anyone please help?
    Thanks very much in advance
     
    Last edited: Feb 28, 2015
  2. jcsd
  3. Feb 28, 2015 #2

    Mark44

    Staff: Mentor

    In other words, you want ##\frac{d^2 y}{dn^2}##, right? That is, the derivative, with respect to n, of dy/dn.
    Since you are differentiating with respect to n, then the derivative of n (with respect to n) is just 1. ##\frac{d}{dn}(n) = 1##.
    You can use either the product rule (that you started with, above) or the quotient rule - your call. The product rule is usually easier to apply.
    I'm not sure I understood what you were asking. If what I wrote isn't what you're looking for, please clarify your question.
     
  4. Feb 28, 2015 #3
    Hi. Thanks. I'm not quite sure what you meant about the d squared y over d n squared. But it sounds like my quotient math above was correct. I wasn't sure if that was right at all.
     
  5. Feb 28, 2015 #4
    Actually. I think I know what you meant. I think I wrote that wrong. I meant [tex]y=\frac{nc(a+b)}{nc+a}[/tex]
     
  6. Feb 28, 2015 #5

    Mark44

    Staff: Mentor

    So all is good, right? You can use either the product rule or the quotient rule for this problem.

    I prefer the Leibniz notation for problems like this, rather than the Newton notation. IOW, I prefer d/dn[nc + a] over (nc+a)′, as it isn't clear in the latter notation that you are differentiating with respect to n.
     
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