December 27th, 2016, 07:50 PM  #1 
Newbie Joined: Dec 2016 From: Lehigh valley, pa Posts: 5 Thanks: 0  Need help with chain rule
Could someone please tell me what it is that I'm not getting.. I attached an image, I hope it loaded properly.

December 27th, 2016, 08:38 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,678 Thanks: 1339 
$y=(52x)^{3}+\dfrac{1}{8}\left(\dfrac{2}{x}+1\right)^4$ $\dfrac{dy}{dx}=3(52x)^{4}\cdot (2) + \dfrac{1}{2}\left(\dfrac{2}{x}+1\right)^3 \cdot \left(\dfrac{2}{x^2}\right)$ $\dfrac{dy}{dx}=\dfrac{6}{(52x)^4}  \dfrac{1}{x^2} \left(\dfrac{2}{x}+1\right)^3$ 
December 27th, 2016, 08:45 PM  #3 
Newbie Joined: Dec 2016 From: Lehigh valley, pa Posts: 5 Thanks: 0 
Thank you so much.

December 28th, 2016, 12:14 AM  #4  
Global Moderator Joined: Dec 2006 Posts: 18,250 Thanks: 1439  Quote:
Let's consider y = (5  2x)^(3). Let u = 5  2x, so that du/dx = 0  2 = 2. As y = u^(3), dy/du = 3u^(4) = 3/u^4, and so dy/dx = (dy/du)(du/dx) = (3/u^4)(2) = 6/u^4 = 6/(5  2x)^4.  
December 30th, 2016, 05:28 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,878 Thanks: 766 
Generally speaking, using the "power" rule, $\displaystyle \frac{du^{n}}{dx}= nu^{n1}\frac{du}{dx}$ with a negative power is far easier than using the "quotient" rule with $\displaystyle \frac{1}{u}$


Tags 
chain, rule 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Chain Rule  jake6390  Calculus  4  May 17th, 2014 05:21 PM 
chain rule constant rule  ungeheuer  Calculus  1  July 30th, 2013 06:10 PM 
Product rule into chain rule  unwisetome3  Calculus  4  October 19th, 2012 02:21 PM 
Chain Rule  arron1990  Calculus  5  May 19th, 2012 07:04 AM 
how do yo solve this one using chain rule with quotient rule  Peter1107  Calculus  1  September 8th, 2011 11:25 AM 