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Math Help - log derivatives

  1. #1
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    log derivatives

    can someone check if I'm doing this right:

    1.)  \frac{d}{dx} \int^{3x+2}_1 \frac{1}{t}dt

    \frac{d}{dx} ln(3x+2)

    \frac{1}{3x+2}*3

    ans:  \frac{3}{3x+2}
    ------------------------------------------
    2.) \int\big(\frac{d}{dx} lnf(x)\big)dx

    \int \frac{1}{f(x)}dx

    ans: lnf(x) + C
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  2. #2
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    Quote Originally Posted by viet View Post
    can someone check if I'm doing this right:

    1.)  \frac{d}{dx} \int^{3x+2}_1 \frac{1}{t}dt

    \frac{d}{dx} ln(3x+2)

    \frac{1}{3x+2}*3

    ans:  \frac{3}{3x+2}
    This looks correct to me, even after I had 6 shots of whiskey. What was I saying again?
    2.) \int\big(\frac{d}{dx} lnf(x)\big)dx

    \int \frac{1}{f(x)}dx

    ans: lnf(x) + C
    But no need to do all that.
    You should not that the integral of the derivative is the original function plus constants. Since the original function was \ln f(x) means the the answer would be \ln f(x) +C.
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  3. #3
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    the 2nd question

    Quote Originally Posted by viet View Post
    can someone check if I'm doing this right:

    2.) \int\big(\frac{d}{dx} lnf(x)\big)dx

    \int \frac{1}{f(x)}dx

    ans: lnf(x) + C
    On the 2nd question
    Attached Thumbnails Attached Thumbnails log derivatives-12jun2007.jpg  
    Last edited by curvature; June 6th 2007 at 07:06 AM.
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