Concept of derivative of the function, Physics

KINEMATICS II

1. The concept of the derivative of the function is exceptionally important. The derivative shows that how fast the function changes when its argument is changed. (Remember that for f ( x) we say that is a function that depends upon the argument x. You should think of as a machine which gives you the value when you input x.)

 

2.  Functions do not always have to be written as f ( x). us where a body is at different times t.

 

3. The derivative of x(t ) at time t can be defined as:

1433_derivative of x.png

2417_derivative of x1.png

4. Now let's see how to calculate the derivative of a simple function such as  x(t ) = t 2 . We should first calculate the difference in x at two slightly different values say, t and t + Δt, while that recall we choose Δt to be extremely small:

606_derivative of x2.png

5. In exactly the same manner you can show that if x(t ) = t n  then:

1879_derivative of x3.png

This is an exceptionally useful result.

Posted Date: 7/26/2012 1:58:14 AM | Location : United States







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