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Find the derivative of (t^2 - 4/t^4)*t^3

  1. Oct 16, 2007 #1
    I have two of these here...

    1. The problem statement, all variables and given/known data
    Find the derivative


    2. Relevant equations
    [tex](t^2-\frac{4}{t^4})*t^3[/tex]


    3. The attempt at a solution
    This is how far I got:
    [tex](t^2-4t(^-4))(t(^3))[/tex]
    [tex](t^2-4t(^-4))(3t(^2))+(t^3)(2t+16t(^-5))[/tex]


    1. The problem statement, all variables and given/known data
    Find the derivative


    2. Relevant equations
    [tex]f(x) = \frac{(6x+5)(x^3-2)}{(3x^2-5)}[/tex]


    3. The attempt at a solution
    This is what I got only:
    [tex](6x+5)(x^3-2)(3x^2-5)(^-1)[/tex]
     
  2. jcsd
  3. Oct 16, 2007 #2

    rock.freak667

    User Avatar
    Homework Helper

    Well for [tex](t^2-\frac{4}{t^4})*t^3[/tex]

    you could just multiply it out and get [tex]t^5+\frac{4}{t}=t^5+4t^{-1}[/tex] and proceed to differentiate w.r.t. t

    for the 2nd one
    [tex]\frac{d}{dx}(uv)=\frac{v\frac{du}{dx}+u\frac{dv}{dx}}{v^2}[/tex]

    by that formula you should see that the end derivative would be a fraction
     
  4. Oct 16, 2007 #3
    always simplify from the beginning if you can

    for 2. take the ln of both sides and expand it then take the derivative
     
  5. Oct 18, 2007 #4
    Allright, thanks. I got both problems worked out correctly now.
     
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