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Derivatives (finance) (view source)
Revision as of 20:14, December 28, 2012
, 20:14, December 28, 2012→Math
In [[calculus]], a derivative is an operation on a function that shows the rate at which the output of the function is changing. The classic example of this is position with respect to time. Say some function f(t) is the position of an object at time t, then the derivative of f(t) would be the velocity of the object at time t, and further, the derivative of the velocity function would be the acceleration of the object at time t. The typical way of writing the derivative of a function f(t) would be f'(t).
In [[calculus]], a derivative is an operation on a function that shows the rate at which the output of the function is changing. The classic example of this is position with respect to time. Say some function f(t) is the position of an object at time t, then the derivative of f(t) would be the velocity of the object at time t, and further, the derivative of the velocity function would be the acceleration of the object at time t. The typical way of writing the derivative of a function f(t) would be f'(t).
A useful application of this is in physics.
The acceleration function a(x) is the derivative of the velocity function, v(x). V(x) is the derivative of the position or displacement function, p(x).
Example:
Displacement given by p(x) = 3x<sup>2</sup>+6x+5
v(x) = p'(x) [shorthand for derivative of p(x) = 6x + 6
a(x) = v'(x) = 6
Thus, if x = 4, assuming the MKS units system for physics, the displacement is 77 m, the velocity is 30 m/s, and the acceleration is 6 m/s<sup>2</sup>.