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Math Help - [SOLVED] Derivative of arctan[x/2]

  1. #1
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    [SOLVED] Derivative of arctan[x/2]

    What is the derivative of arctan(x/2)??

    I had a test today, so I eliminated some of the MC answers, and I guessed it was 2/x^2+4, but didn't show my work.. How do I do this?
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  2. #2
    Member Mentia's Avatar
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    Yeah so the derivative of arctan(x) is 1/(x^2+1)

    If you have arctan(x/2) you can use the chain rule:

    (d/dx) arctan(x/2) = [1/([x/2]^2+1)]*(1/2) = 1/([x^2]/2+1)

    ->  \frac{1 }{ \frac{ { x}^{2 }  }{2 } +2 } =  \frac{2 }{ {x}^{ 2}  + 4}

    so you got it right
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