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Math Help - derivative of ln

  1. #1
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    derivative of ln

    im currently trying to find the derivative of
    f(x)= ln[x+(4+x)^(1/2)]
    im a little confused on how to approach this...any help would be greatly appreciated for get me started! thx
    ln(x) + [1/2]ln(4+x) is incorrect right?
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  2. #2
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    Quote Originally Posted by nuclear123 View Post
    im currently trying to find the derivative of
    f(x)= ln[x+(4+x)^(1/2)]
    im a little confused on how to approach this...any help would be greatly appreciated for get me started! thx
    ln(x) + [1/2]ln(4+x) is incorrect right?

    in general

    f = ln g

    f ' = \frac{g'}{g}


    f(x) = \ln (x+(4+x^2)^{\frac{1}{2}})

    let

    g(x) = x + (4+x^2)^{\frac{1}{2}}

    f(x) = \ln g(x) so f'(x) = \frac{g'(x)}{g(x)}

    first find
    g'(x) = 1 + \frac{1}{2} (2x) (4+x^2)^\frac{-1}{2}

    so

    f'(x) = \frac{g'(x)}{g(x)} = \frac{1 + \frac{1}{2} (2x) (4+x^2)^\frac{-1}{2}}{x + (4+x^2)^{\frac{1}{2}}}

    simplify it
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