Results 1 to 2 of 2

Math Help - differentiation w/fractions

  1. #1
    Junior Member
    Joined
    Mar 2006
    Posts
    40

    differentiation w/fractions

    Directions: Differentiate the given function doing as much of the computation as possible in your head and simplify your answer.

    Problem: f(x) = square root of x^3 + 1/square root of x^3

    My solution: f(x) = 3x^-1/2 + 3/2square root of x^5 = 3/2 square root of x + 3/2 square root of x^5.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,803
    Thanks
    692
    Hello, Becky!

    Differentiate the given function doing as much of the computation as possible in your head and simplify your answer.

    Problem: f(x) \;= \;\sqrt{x^3} + \frac{1}{\sqrt{x^3}}
    We have: f(x) \;= \;x^{\frac{3}{2}} + x^{-\frac{3}{2}}

    Differentiate: f'(x)\;=\;\frac{3}{2}x^{\frac{1}{2}} - \frac{3}{2}x^{-\frac{5}{2}}

    Factor: f'(x) \;= \;\frac{3}{2}x^{-\frac{5}{2}}\left(x^3 - 1\right) \;= \;\frac{3(x^3 - 1)}{2x^{\frac{5}{2}}} \;= \;\frac{3(x^3 - 1)}{2\sqrt{x^5}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 28th 2010, 09:53 AM
  2. Differentiation by partial fractions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 25th 2009, 05:01 AM
  3. Simplifying Fractions over fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 28th 2009, 10:20 AM
  4. Differentiation of fractions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 17th 2008, 03:06 AM
  5. simplifing fractions over fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 16th 2007, 01:57 PM

Search Tags


/mathhelpforum @mathhelpforum