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Math Help - Doubt

  1. #1
    Member srirahulan's Avatar
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    Post Doubt

    differentiate respect to (x) 2^x In this case my friends do like this


    y=2^x
    lny=xln2
    Then differentiate both side respect to x

    In the second step how we take a variable in front of log,we only take a constant to the front of log.. please give me a solution
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  2. #2
    MHF Contributor MarkFL's Avatar
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    St. Augustine, FL.
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    Re: Doubt

    The logarithmic property:

    \log_a\left(b^c \right)=c\cdot\log_a(b)

    is valid whether c is a constant or variable.
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  3. #3
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    Erewhon
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    Re: Doubt

    Quote Originally Posted by srirahulan View Post
    differentiate respect to (x) 2^x In this case my friends do like this


    y=2^x
    lny=xln2
    Then differentiate both side respect to x

    In the second step how we take a variable in front of log,we only take a constant to the front of log.. please give me a solution
    y(x)=2^x=(e^{\ln(2)})^x=e^{x\ln(2)}

    .
    Thanks from MarkFL
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