Derivative of unit step function?

How would I find the derivative of a unit step function? I understand that the unit impulse function will be used but I'm not sure how to use it.

I am trying to find the derivative of this:

$v(t) = u(t+1) - 2u(t) + u(t-1)$

$u(t) = 0$ when $t < 0$

$u(t) = 1$ when $t > 0$

The relationship between unit step function and impulse function:

δ(n) = u(n) - u(n-1)

$ δ(t)=du(t)/dt $

1 Answer

The derivative of unit step $u(t)$ is Dirac delta function $\delta(t)$, since an alternative definition of the unit step is using integration of $\delta(t)$ here.

$$u(t)=\int_{-\infty}^{t}\delta(\tau)d\tau$$

Hence,

$$\frac{du}{dt}=\delta(t+1)-2\delta(t)+\delta(t-1)$$