What is the derivative of this

  • #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
 

Answers and Replies

  • #2
Pengwuino
Gold Member
5,009
16
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] ?
 
  • #3
537
3
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

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:
  • #4
35,236
7,056
hey guys
whats is the derivative of you are asked to integrate;
x(t) = pi / t2

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.
 
  • #5
what would be the derivative if you are asked to differentiate x(t) = pi / t^2
 
  • #6
537
3
what would be the derivative if you are asked to differentiate x(t) = pi / t^2

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?
 
  • #7
35,236
7,056
Are you being asked to differentiate the function you gave, or integrate (i.e. anti-differentiate)?
I rest my case.
 
  • #8
1,015
70
what would be the derivative if you are asked to differentiate x(t) = pi / t^2

What rules of differentiation do you know? Or do you just know the definition of the derivative of a function?
 
  • #9
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Do you know that pi/t^2= pi t^{-2}? Do you know the derivative of t^n?
 

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