Derivative of unit step function

Question

The ramp function is given by r(t)=tu(t) If we differentiate ramp ,we get unit step function. That is, u(t)=1 So the derivative of unit step function is definitely 0 since u(t) is constant over the positive t axis. But its derivative is actually del(t) How is this possible? Please explain this

Answer 1

There is a steep and abrupt increase in the amplitude of the unit step function $u(t)$ at $t=0$, so the slope or the derivative of $u(t)$ will have a infinite slope at $t=0$ hence the derivative peaks at $t=0$ therefore it is a delta function