My Math Forum Derivative without using properties of logarithms

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 October 3rd, 2014, 08:08 PM #1 Member   Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4 Derivative without using properties of logarithms y = ln[(2x+8 ) / ( 8x+25)] After deriving, I come to $\displaystyle \frac{1}{\dfrac{2x+8}{8x+25}}\left(-\frac{14}{(8x+25)^2}\right)$ Could someone fully show me how to simplify this further? EDIT: I get to negative 7/(x+4)(8x+25)^3 but wolfram says that ^3 is not supposed to be there for (8x+25).... Last edited by MarkFL; October 3rd, 2014 at 10:47 PM. Reason: Restore gutted content
 October 3rd, 2014, 10:45 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,193 Thanks: 504 Math Focus: Calculus/ODEs What you want is: $\displaystyle \frac{1}{\dfrac{2x+8}{8x+25}}\left(-\frac{14}{(8x+25)^2}\right)=-\frac{2\cdot7(8x+25)}{2(x+4)(8x+25)^2}=-\frac{7}{(x+4)(8x+25)}$ By the way, please do not edit a post once you have solved the question to remove the original question. Gutting a thread this way leaves behind a useless post.

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