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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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derivative, logarithms, properties 
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