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Math Help - find the derivative

  1. #1
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    Post find the derivative

    find the derivative

    g(x)= ln x^(3/4)/((3x+5)^5)
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  2. #2
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    Quote Originally Posted by Sally_Math View Post
    find the derivative

    g(x)= ln x^(3/4)/((3x+5)^5)
    what an ugly function ...

    g(x) = \frac{3}{4} \cdot \frac{\ln{x}}{(3x+5)^5}

    g'(x) = \frac{3}{4} \cdot \frac{(3x+5)^5 \cdot \frac{1}{x} - \ln{x} \cdot 15(3x+5)^4}{(3x+5)^{10}}

    g'(x) = \frac{3}{4} \cdot \frac{(3x+5) \cdot \frac{1}{x} - \ln{x} \cdot 15}{(3x+5)^6}

    g'(x) = \frac{3(3x+5) - 15x\ln{x}}{4x(3x+5)^6}
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  3. #3
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    Quote Originally Posted by skeeter View Post
    what an ugly function ...

    g(x) = \frac{3}{4} \cdot \frac{\ln{x}}{(3x+5)^5}

    g'(x) = \frac{3}{4} \cdot \frac{(3x+5)^5 \cdot \frac{1}{x} - \ln{x} \cdot 15(3x+5)^4}{(3x+5)^{10}}

    g'(x) = \frac{3}{4} \cdot \frac{(3x+5) \cdot \frac{1}{x} - \ln{x} \cdot 15}{(3x+5)^6}

    g'(x) = \frac{3(3x+5) - 15x\ln{x}}{4x(3x+5)^6}
    thanks but is it the same for that the problem says ln((x^3/4)/(3x+5)^5)
    Is this problem the same as the above


    and thanks again
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  4. #4
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    Quote Originally Posted by Sally_Math View Post
    thanks but is it the same for that the problem says ln((x^3/4)/(3x+5)^5)
    Is this problem the same as the above


    and thanks again
    you tell me ...

    is \frac{\ln{x^{\frac{3}{4}}}}{(3x+5)^5} = \frac{3}{4} \cdot \frac{\ln{x}}{(3x+5)^5} ?
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  5. #5
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    Quote Originally Posted by skeeter View Post
    you tell me ...

    is \frac{\ln{x^{\frac{3}{4}}}}{(3x+5)^5} = \frac{3}{4} \cdot \frac{\ln{x}}{(3x+5)^5} ?
    yes it is the same but I just wanted to ask bcz my eqn is ln(the eq.)
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  6. #6
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    Quote Originally Posted by Sally_Math View Post
    find the derivative

    g(x)= ln x^(3/4)/((3x+5)^5)

    ...

    yes it is the same but I just wanted to ask bcz my eqn is ln(the eq.)
    then you should have used brackets to indicate ln[your expression], like so ...

    g(x)= ln[x^(3/4)/((3x+5)^5)]

    or ...

    g(x) = \ln\left[\frac{x^{\frac{3}{4}}}{(3x+5)^5}\right]

    use the laws of logs to break up the expression into several logs, then find the derivative of each logarithmic term.

     <br />
\ln\left[\frac{x^{\frac{3}{4}}}{(3x+5)^5}\right] = \frac{3}{4}\ln{x} - 5\ln(3x+5)
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