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Differentiation of a polynomial function

  1. Nov 16, 2011 #1
    Hi guys

    I'm getting into a little trouble when differentiating polynomial functions.

    How do you differentiate

    f(x)=ax+b/cx+d ?

    Is there other ways of calculating this apart from the chain rule ?


    Thanks for any help.
     
  2. jcsd
  3. Nov 16, 2011 #2

    HallsofIvy

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    Surely by the time you are taking Calculus you should know that what you give is NOT a polynomial!! And I can't imagine why you would think about the chain rule. That is a quotient so use the quotient rule.
     
  4. Nov 17, 2011 #3
    Re: Differentiation of a rational function

    Sorry I messed up.
    What I meant was a "rational" function.

    Are "rational" and "quotient" synonymous ?

    By applying the quotient rule, I get

    (ax+b/cx+d)'= [(cx+d)(ax+b)'-(ax+b)(cx+d)'] / (cx+d)^2

    = [a(cx+d)-c(ax+b)] / (cx+d)^2

    how to proceed ?
     
  5. Nov 17, 2011 #4

    Stephen Tashi

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    You can multiply the terms in the top of the fraction [itex] \frac{a(cx+d) - c(ax+b)}{(cx+d)^2}[/itex] and then combine like terms. I don't see anything that "simplifies" beyond that.

    A point about notation, you should write the original function as (ax+b)/(cx+d) to mean [itex] \frac{ax+b}{cx+d} [/itex] instead of writing it as (ax +b/cx + d}, which means [itex] ax + \frac{b}{c} x + d [/itex].

    Better yet, look at the sticky thread:
    Physics Forums > PF Lounge > Forum Feedback & Announcements
    LaTeX Guide: Include mathematical symbols and equations in a post
     
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