Results 1 to 3 of 3

Thread: log derivatives

  1. #1
    Member
    Joined
    Nov 2005
    Posts
    172

    log derivatives

    can someone check if I'm doing this right:

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

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

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

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

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

    ans: $\displaystyle lnf(x) + C$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by viet View Post
    can someone check if I'm doing this right:

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

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

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

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

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

    ans: $\displaystyle lnf(x) + C$
    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 $\displaystyle \ln f(x)$ means the the answer would be $\displaystyle \ln f(x) +C$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2007
    Posts
    237

    the 2nd question

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

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

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

    ans: $\displaystyle lnf(x) + C$
    On the 2nd question
    Attached Thumbnails Attached Thumbnails log derivatives-12jun2007.jpg  
    Last edited by curvature; Jun 6th 2007 at 06:06 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivatives and Anti-Derivatives
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Feb 6th 2011, 06:21 AM
  2. Replies: 1
    Last Post: Jul 19th 2010, 04:09 PM
  3. Derivatives with both a and y
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 4th 2009, 09:17 AM
  4. Replies: 4
    Last Post: Feb 10th 2009, 09:54 PM
  5. Trig derivatives/anti-derivatives
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 10th 2009, 01:34 PM

Search Tags


/mathhelpforum @mathhelpforum