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Find the derivative of arctan(6x)

  1. Mar 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the derivative of arctan(6x).

    2. Relevant equations

    3. The attempt at a solution
    Ok, I know the derivative of arctan(x) is 1/(x^2 + 1).

    So I am trying to make the substitution u = 6x.

    Then the derivative of arctan(u) should be 1/(u^2 + 1)... and therefore 1/(36x^2 +1).

    But that's not right... what am I doing wrong?
  2. jcsd
  3. Mar 10, 2009 #2


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    Homework Helper

    if you make the subsitition u(x) = 6x

    then you have
    [tex] \frac{d}{dx} arctan(u(x)) [/tex]

    so you need to use the chain rule...
  4. Mar 10, 2009 #3
    I can't read your equation...
  5. Mar 10, 2009 #4
    Okay, so:

    1/(u^2 +1) multiplied by the derivative of u?
  6. Mar 10, 2009 #5


    User Avatar
    Science Advisor

    Yes. And since u= 6x, its derivative is ?
  7. Mar 10, 2009 #6
    6/(36x^2 +1)?

    Thank you!
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