- #1
Will
[SOLVED] Derivative of unit step function
How does one do this, for example x= e^(-3t)u(t-4); how do you get x' ??
How does one do this, for example x= e^(-3t)u(t-4); how do you get x' ??
x(t) = e^(-3t) (for t > 4)
0 (for t < 4)
x'(t) = (-3) e^(-3t) (for t > 4)
0 (for t < 4)
The derivative of a unit step function is a mathematical concept that represents the rate of change of the unit step function with respect to its input variable. It is defined as the limit of the change in the function's output divided by the change in its input as the change in the input approaches zero.
To find the derivative of a unit step function, you can use the definition of the derivative or apply the derivative rules for step functions. These rules state that the derivative of a step function is zero everywhere except at the step, where it is undefined.
The value of the derivative of a unit step function at the step is undefined. This is because the step function is discontinuous at the step, and the derivative is not defined for discontinuous functions.
No, the derivative of a unit step function is not a continuous function. This is because the unit step function is discontinuous at the step, and the derivative is not defined at that point. However, the derivative is continuous everywhere else.
The physical interpretation of the derivative of a unit step function is the instantaneous rate of change of a quantity that changes abruptly at a specific point. This can be seen in real-world scenarios such as measuring the speed of an object that suddenly changes direction at a certain time.