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Math Help - Some derivative questions

  1. #1
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    Some derivative questions

    ,

    -----------

    ,
    ------------


    Find the equation of the tangent line of the function
    at the point .

    ------------------


    Let .



    --------------


    A)If , find .



    B) Find .
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by redraider717 View Post
    ,

    -----------

    ,
    ------------
    You need to know that \frac{d}{dx} e^x = e^x and that \sqrt[3]{x} = x^{1/3}.

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by redraider717 View Post
    Find the equation of the tangent line of the function
    at the point .
    You need to know that \frac{d}{dx}ln(x) = \frac{1}{x} = x^{-1}.

    So
    f(x) = x^{-1} + x^{-2} + ln(x)

    f^{\prime}(x) = (-1)x^{-2} + (-2)x^{-3} + x^{-1}

    So
    f^{\prime}(1) = -(1)^{-2} - 2(1)^{-3} + (1)^{-1} = -2

    So the slope of the tangent line to the function f(x) at x = 1 is -2.

    What point is the tangent line passing through? Well, it passes through the point on the function at x = 1:
    f(1) = (1)^{-1} + (1)^{-2} + ln(1) = 2

    So we want a line with a slope of -2 that passes through the point (1, 2).

    I leave the rest to you.

    -Dan
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