What is the derivative of this

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In summary: Apply the chain rule and the power rule.In summary, the derivative of x(t) = pi / t^2 can be found by applying the power rule for derivatives and the chain rule, as the function can be rewritten as x(t) = pi * t^(-2).
  • #1
JakePearson
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hey guys
whats is the derivative of you are asked to integrate;

x(t) = pi / t2

i don't have a rule for this, so i can't integrate it :( help
 
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  • #2
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
JakePearson said:
hey guys
whats is the derivative of you are asked to integrate;

x(t) = pi / t2

i don't have a rule for this, so i can't 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
JakePearson said:
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
JakePearson said:
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
n!kofeyn said:
Are you being asked to differentiate the function you gave, or integrate (i.e. anti-differentiate)?
I rest my case.
 
  • #8
JakePearson said:
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
Do you know that pi/t^2= pi t^{-2}? Do you know the derivative of t^n?
 

What is the derivative of a polynomial function?

The derivative of a polynomial function is found by multiplying each term by its exponent and then subtracting 1 from the exponent. For example, the derivative of 2x^3 + 5x^2 - 3x + 1 would be 6x^2 + 10x - 3.

What is the derivative of a trigonometric function?

The derivative of a trigonometric function depends on the specific function. For example, the derivative of sine is cosine, the derivative of cosine is negative sine, and the derivative of tangent is secant squared.

What is the derivative of a logarithmic function?

The derivative of a logarithmic function is found by using the power rule. For example, the derivative of ln(x) is 1/x.

What is the derivative of a composite function?

The derivative of a composite function is found by using the chain rule. This involves taking the derivative of the outer function and multiplying it by the derivative of the inner function. For example, the derivative of (2x^2 + 3)^5 would be 5(2x^2 + 3)^4 * 4x.

What is the derivative of an exponential function?

The derivative of an exponential function is found by using the power rule and multiplying it by the natural log of the base. For example, the derivative of 5^x would be 5^x * ln(5).

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