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Math Help - Derivative of: ∫1/x dx = ln IxI help...

  1. #1
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    Question Derivative of: ∫1/x dx = ln IxI help...

    Could someone show me how to get the derivative of both sides of this equation? I can't quite seem to figure it out. I have an answer, but I'm not sure it is not correct. Thanks for looking.

    Here is what I have so far:
    y= ln x, so x= e^y
    which gives 1= e^y dy/dx
    then 1/e^y= dy/dx
    which gives 1/e^lnx=dy/dx
    and lastly dy/dx= 1/x
    Good or not so good?
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  2. #2
    Super Member Showcase_22's Avatar
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    \int \frac{1}{x}~dx= \ln x

    Differentiating both sides gives \frac{1}{x}=\frac{1}{x}.

    Why do you need to do this?
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  3. #3
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    it is...

    part of an assignment that I am stuck on. Could you show me how to go through the steps or no?
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  4. #4
    Super Member Showcase_22's Avatar
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    Well there aren't really steps to it.

    From <br /> <br />
\int \frac{1}{x}~dx= \ln x<br />
we know that \frac{d}{dx} \ln x =\frac{1}{x} by the fundamental theorem of calculus.

    We also know (from the fundamental theorem of calculus) that \frac{d}{dx}\int \frac{1}{x}~dx= \frac{1}{x}

    So you can just apply this to both sides of the equation.
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  5. #5
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    thanks!

    Thanks for the help.
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