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Math Help - Find dy/dx

  1. #1
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    Find dy/dx

    y=\log{(6x)}
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  2. #2
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    Quote Originally Posted by Jim Marnell View Post
    y=\log{(6x)}
    This depends on if you mean \log_{10}(x) or \log_{e}(x)=\ln(x)
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  3. #3
    MHF Contributor Calculus26's Avatar
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    I assume by log(6x) you are referring to the base 10 logarithm

    y = log(6x) = log(6) +log(x) = log(6) +ln(x)/ln(10)

    dy/dx = 1/[xln(10]
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  4. #4
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    U need to define a base for this log (6x) ..... for example


    log_{\alpha}(6x)

    After this u will have:

    y=log_{\alpha}(6x)=\frac{ln(6x)}{ln(\alpha)}

    \Rightarrow dy=\frac{1}{6xln(\alpha)}*(6x)' dx

    \Rightarrow dy=\frac{1}{6xln(\alpha)}*6 dx

    \Rightarrow dy=\frac{1}{xln(\alpha)} dx

    \Rightarrow dy=\frac{1}{xln(\alpha)} dx

    \Rightarrow \frac{dy}{dx}=\frac{1}{xln(\alpha)}

    Have a nice day

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