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Math Help - derivatives of log/ln

  1. #1
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    derivatives of log/ln

    Can somebody help me find the derivative of :


    m = 2(2)^(-t/15)

    when t = 5...

    please and thank you
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    ok

    Quote Originally Posted by go.leafs.go.89 View Post
    Can somebody help me find the derivative of :


    m = 2(2)^(-t/15)

    when t = 5...

    please and thank you
    you have f(t)=2\cdot{2^{\frac{-t}{15}}=2^{\frac{-t}[15}+1} so if we take the ln both sides we get ln(f(t))=\bigg[\frac{-t}{15}+1\bigg]\cdot{ln(2)} so by taking the derivative of each side we get \frac{f'(t)}{f(t)}=\frac{-ln(2)}{15} and since f(t) is our original equation we have f'(t)=\frac{-ln(2)2^{\frac{-t}{15}+1}}{15}
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  3. #3
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    Quote Originally Posted by go.leafs.go.89 View Post
    Can somebody help me find the derivative of :


    m = 2(2)^(-t/15)

    when t = 5...

    please and thank you
    Try expressing the two raised to a power as e raised to a power:

    m = 2~2^{-t/15}=2~e^{- \frac{t~\ln(2)}{15}}

    RonL
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  4. #4
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    hm i dont understand how the plus 1 came?
    and also .. we didn't learn about implicit differentiation ..
    is there any other way to do this question?
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Haha

    Quote Originally Posted by go.leafs.go.89 View Post
    hm i dont understand how the plus 1 came?
    and also .. we didn't learn about implicit differentiation ..
    is there any other way to do this question?
    You know the name of something you never learned? ok...but still the +1 came from the fact taht 2\cdot{2^{n}}=2^{n+1} and you can do what CaptainBlack said and use the rules of \frac{D[e^{u(x)}]}{dx}
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