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Math Help - another derivative..

  1. #1
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    another derivative..

    will someone do a step by step so I can try and teach myself this stuff..


    Let
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  2. #2
    MHF Contributor
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    \frac{d}{dx} \tan^{-1} x = \frac{1}{1 + x^2}

    The chain rule:
    \frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)

    Let f(x) = \tan^{-1} x, g(x) = \cos (7x)

    \frac{d}{dx} \tan^{-1} (\cos (7x)) =

    \frac{1}{1 + (\cos (7x))^2} \cdot \frac{d}{dx} \cos (7x) =

    \frac{-\sin (7x)}{1 + (\cos (7x))^2} \cdot \frac{d}{dx} (7x) =

    \frac {-7 \sin (7x)}{1 + (\cos (7x))^2}
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  3. #3
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    thank you very much
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