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Calculus I - Differentiation

  1. Oct 26, 2009 #1
    1. The problem statement, all variables and given/known data
    (x^(3)+2x) / (x^(2)-5) d/dx = ?


    2. Relevant equations
    d/dx (f/g) = (g d/dx (f) - f d/dx (g)) / g^2


    3. The attempt at a solution

    d/dx y = { (x^(2)-5) d/dx (x^(3)+2x) - (x^(3)+2x) d/dx (x^(2)-5) } / (x^(2)-5)^2

    This is where it gets complicated for me.

    { (x^(2)-5)(2x^(2)+2) - (x^(3)+2x)(2x) } / (x^(2)-5)^2

    I am pretty sure this is at least close, if it is wrong please tell me where I went wrong, and if it is right but not simplified can you explain how to simplify it further.

    Thank you in advance, I hope that I gave you appropriate information.
     
  2. jcsd
  3. Oct 26, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's almost it. Except d/dx x^(3) is 3x^(2), not 2x^(2). About the only thing you can do to simplify is expand the products in the numerator and add them.
     
  4. Oct 26, 2009 #3

    Mark44

    Staff: Mentor

    The only mistake I noticed was where you have d/dx(x^3 + 2x) = 2x^2 + 2. That should be 3x^2 + 2.

    [tex]\frac{dy}{dx}~=~\frac{(x^2 - 5)(3x^2 + 2) - (x^3 + 2x)(2x)}{(x^2 - 5)^2}[/tex]

    You might get some simplification if you multiply the two products in the numerator and then combine like terms.
     
  5. Oct 26, 2009 #4
    Yep that was a careless typing error, thank you for validating.
     
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