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Simple Chain Rule Question

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Use chain rule to find the derivative of f(x)= sin(x)/(1+x^2)

    2. Relevant equations

    Chain Rule (f(g(x)))'*g'(x)

    3. The attempt at a solution
    y'(x)= cos (x)/(1+x^2)* (1-x^2)/((1+x^2)^2)

    I just want to make sure I am doing it correctly and this would be acceptable as a final answer.
  2. jcsd
  3. Mar 4, 2013 #2


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    Hello parents. Welcome to PF !

    Is the function [itex]\ \displaystyle f(x)=\frac{\sin(x)}{1+x^2} \,,[/itex]

    or is it [itex]\ \displaystyle f(x)=\sin\left(\frac{x}{1+x^2}\right) \ ?[/itex]
  4. Mar 4, 2013 #3
    Sorry! I see how that can be confusing. It's [itex]\ \displaystyle f(x)=\sin\left(\frac{x}{1+x^2}\right) [/itex]

    I am working on trying to put in equations correctly
  5. Mar 4, 2013 #4
    Make the equation f(u)=sin(u). Then take the derivative of sin(u) then multiply by the derivative of u.

    Last edited: Mar 4, 2013
  6. Mar 4, 2013 #5
    Your answer looks good to me.
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