Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Simple differentiation question

  1. #1
    Senior Member
    Joined
    Oct 2009
    Posts
    295
    Thanks
    9

    Simple differentiation question

    s(t)=\frac{a(t)'}{a(t)}

    If

    s(t)=\frac{4}{t+3}

    Find a(t)

    To me a(t) would just be (t+3)^4

    But the book has \frac{t+3}{3}^4

    How'd the book get that answer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,507
    Thanks
    1403

    Re: Simple differentiation question

    Quote Originally Posted by downthesun01 View Post
    s(t)=\frac{a(t)'}{a(t)}

    If

    s(t)=\frac{4}{t+3}

    Find a(t)

    To me a(t) would just be (t+3)^4

    But the book has \frac{t+3}{3}^4

    How'd the book get that answer?
    \displaystyle \begin{align*} \frac{4}{t + 3} &= \frac{1}{a}\, \frac{da}{dt} \\ \int{\frac{4}{t + 3}\,dt} &= \int{\frac{1}{a}\,\frac{da}{dt}\,dt} \\ 4\ln{|t + 3|} + C_1 &= \int{\frac{1}{a}\,da} \\ 4\ln{|t + 3|} + C_1 &= \ln{|a|} + C_2 \\ 4\ln{|t + 3|} + C_1 - C_2 &= \ln{|a|} \\ e^{4\ln{|t+3|} + C_1 - C_2} &= |a| \\ e^{C_1 - C_2} e^{\ln{\left|t +3 \right|^4}} &= |a| \\ a &= C \left( t + 3 \right) ^4 \textrm{ where }C = \pm e^{C_1 - C_2} \end{align*}
    Thanks from downthesun01
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: December 22nd 2010, 03:21 AM
  2. Simple Differentiation Question
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 23rd 2010, 11:08 PM
  3. Replies: 2
    Last Post: November 12th 2009, 03:09 PM
  4. A simple ln differentiation question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 26th 2009, 03:30 AM
  5. Simple Differentiation..
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 2nd 2007, 06:50 PM

Search Tags


/mathhelpforum @mathhelpforum