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What is the derivative of this

  1. Jul 24, 2009 #1
    hey guys
    whats is the derivative of you are asked to integrate;

    x(t) = pi / t2

    i dont have a rule for this, so i cant integrate it :( help
     
  2. jcsd
  3. Jul 24, 2009 #2

    Pengwuino

    User Avatar
    Gold Member

    pi is just a constant so it's simply the integral of [tex]\frac{1}{{t^2 }}[/tex] that you're looking at. What function, when differentiated, results in [tex]\frac{\pi }{{t^2 }}[/tex] ?
     
  4. Jul 24, 2009 #3
    Sure you have a rule: the power rule for integration. If c is a constant and n is not equal to -1, then
    [tex]
    \int cx^n \,dx = \frac{cx^{n+1}}{n+1} + C.
    [/tex]

    Pi is just a constant. Can you write the function x(t) as x(t)=pi*tn for some n, and then apply the above rule?
     
    Last edited: Jul 24, 2009
  5. Jul 24, 2009 #4

    Mark44

    Staff: Mentor

    Someone looking at your question would probably be confused about what you are asking. At first appearances it looks like you want the derivative of the function you show, but the "asked to integrate" part would throw most people off.

    For your own sake and for the sakes of the people who are trying to help you, try to ask your questions in the clearest way you can.
     
  6. Jul 24, 2009 #5
    what would be the derivative if you are asked to differentiate x(t) = pi / t^2
     
  7. Jul 24, 2009 #6
    Are you being asked to differentiate the function you gave, or integrate (i.e. anti-differentiate)?

    To integrate, follow my advice above. To differentiate, apply the same advice to the power rule for derivatives. If c is a constant, n is any number (positive or negative), and f(x)=cxn, then f'(x)=cnxn-1. To differentiate your function x(t), can you write it as x(t)=pi*tn, for some number n?
     
  8. Jul 24, 2009 #7

    Mark44

    Staff: Mentor

    I rest my case.
     
  9. Jul 24, 2009 #8
    What rules of differentiation do you know? Or do you just know the definition of the derivative of a function?
     
  10. Jul 24, 2009 #9

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Do you know that pi/t^2= pi t^{-2}? Do you know the derivative of t^n?
     
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