1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Chain Rule Problem

  1. Sep 21, 2009 #1
    1. The problem statement, all variables and given/known data
    I need to find the derivative of:

    [tex]y=\left(4x+3\right)^{4}\cdot\left(x+1\right)^{-3}[/tex]


    2. Relevant equations
    Chain Rule
    Quotient or Product Rule

    3. The attempt at a solution
    So I tried to use quotient rule because

    [tex]\left(4x+3\right)^{4}\cdot\left(x+1\right)^{-3}=\frac{\left(4x+3\right)^{4}}{\left(x+1\right)^{3}}[/tex]

    thus by quotient rule

    [tex]y=\frac{\left(4x+3\right)^{4}}{\left(x+1\right)^{3}}, \frac{dy}{dx}=\frac{\left[\left(x+1\right)^{3}\cdot4\left(4x+3\right)^{3}\cdot4\right]-\left[\left(4x+3\right)^{4}\cdot3\left(x+1\right)^{2}\cdot1\right]}{\left[\left(x+1\right)^{3}\right]^{2}}[/tex]

    [tex]=\frac{\left[16\left(4x+3\right)^{3}\cdot\left(x+1\right)^{3}\right]-\left[3\left(4x+3\right)^{4}\cdot\left(x+1\right)^{2}\right]}{\left(x+1\right)^{6}}[/tex]

    [tex]=\frac{16\left(4x+3\right)^{3}\cdot\left(x+1\right)^{3}}{\left(x+1\right)^{6}}-\frac{3\left(4x+3\right)^{4}\cdot\left(x+1\right)^{2}}{\left(x+1\right)^{6}}[/tex]

    [tex]=\frac{16\left(4x+3\right)^{3}}{\left(x+1\right)^{2}}-\frac{3\left(4x+3\right)^{4}}{\left(x+1\right)^{3}}[/tex]

    I don't know where to go from here... I know that the answer to the problem is

    [tex]\frac{\left(4x+3\right)^{3}\left(4x+7\right)}{\left(x+1\right)^{4}}[/tex]

    I just don't know how the hell I am supposed to get there.
     
  2. jcsd
  3. Sep 21, 2009 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Instead of breaking the fraction into two on the third line, factor everything you can in the numerator on the second line and see what happens.
     
  4. Sep 21, 2009 #3
    Good god I feel foolish. It was really that simple. The thought, "why didn't I think of that?" comes to mind. :) Thank you for your help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Chain Rule Problem
  1. Chain Rule Problem (Replies: 3)

  2. Chain Rule Problem (Replies: 4)

Loading...