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Thread: Doubt

  1. #1
    Member srirahulan's Avatar
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    Post Doubt

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


    $\displaystyle y=2^x$
    $\displaystyle lny=xln2$
    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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    Re: Doubt

    The logarithmic property:

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

    is valid whether $\displaystyle c$ is a constant or variable.
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  3. #3
    Senior Member zzephod's Avatar
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    Re: Doubt

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


    $\displaystyle y=2^x$
    $\displaystyle lny=xln2$
    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
    $\displaystyle y(x)=2^x=(e^{\ln(2)})^x=e^{x\ln(2)}$

    .
    Thanks from MarkFL
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