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Forgot my chain rule T.T

  1. Feb 17, 2007 #1
    1. The problem statement, all variables and given/known data
    y = 2x / (1+x^2)^2

    Find dy/dx

    2. Relevant equations
    Chain rule


    3. The attempt at a solution
    I completely forgot how to apply the chain rule.. I mean, I can always apply the quotient rule, but I'm sure this is 1000 times easier if you can apply the chain rule. Do you do something like

    u = 1+x^2
    du = 2x

    so

    y = du/u

    But I may be getting confused with substitution rule with integration.. it's been a while since I touched calculus.. any suggestions?
     
  2. jcsd
  3. Feb 17, 2007 #2
    Chain rule goes something like
    dy/dx=dy/du*du/dv*......*df/dx .

    It is usually used when you when you have a nested combination of functions, ie functions within functions.

    For your question, you need to use both the quotient rule as well as the chain rule ( (1+x^2)^2, which is the funtion 1+x^2 within a squaring function ) .

    Can you finish your problem now ?
     
  4. Feb 17, 2007 #3
    Right.. that's the BRUTE force way to do it.

    I was wondering if there was a way to finish this without even applying the quotient rule
     
  5. Feb 17, 2007 #4
    if you dont want to use the quotient rule you can bring the denominator up top so:[tex] y= 2x (1+x^2)^{-2}[/tex] now use the product rule
     
  6. Feb 17, 2007 #5

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, just write the expression as 2x(1+x2)-2, and use the product rule on this.
     
  7. Feb 17, 2007 #6
    I guess that's true, but when I saw the relating terms, I was thinking this could be solved by ONLY using chain rule.

    I guess it's impossible.
     
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