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Math Help - Derivative question

  1. #1
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    Derivative question

    Hello!

    I am having trouble deriving y = cot(arctan(x))

    I got dy/dx = [-1+tan^2(arctan(x))]/[tan^2(arctan(x))(1+x^2)]



    I used the chain rule for the overall equation, and I also used

    Does this look correct? Or am I way off? Perhaps, can this be simplified further?


    Any help is much appreciated,

    Dranalion
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  2. #2
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    cot(arctan(x)) = \frac{1}{tan(arctan(x))} = ?
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  3. #3
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    Using this, I got:

    dy/dx = [(-sec^2(arctan(x))/(1+x^2)] / [tan^2(arctan(x)]

    I seem even more tangled!

    Am I on the right track? Can this be simplified further?

    Any help much appreciated
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  4. #4
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    You should recall that by definition, tan(arctan(x)) = arctan(tan(x)) = x
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  5. #5
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    So does: y = cot(arctan(x))

    dy/dx = -1/x^2


    Sound right?
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  6. #6
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    Yep.
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