Derivative of t per unit step - meaning of $t\delta (t)$ I derived the function ($u(t)$ is the unit step):

$$x(t)=t \space u(t)$$

$$dx/dt=1 \space u(t)+t \space \delta(t)$$

What is the graphical meaning of the second term?

Thank you very much.
The function $x(t)$ is a ramp and is not differentiable at $t=0$ (the left and right derivatives differ). The term $t\,\delta(t)$ accounts for that non-differentiability (the Heaviside step takes a finite value at $t=0$).

Graphically speaking, you can picture it as two infinitely close Dirac deltas with opposite signs (which implements a differentiation operator by convolution).
$\delta (t)$ is the Dirac delta function (well... distribution). This "function" assumes the value $\infty$ at zero and is zero everywhere else. The funny thing is

$$\int_{\mathbb{R}} \delta (t) \ dt = 1 $$

I suggest consulting the Wiki page. The Dirac delta is like a point pulse.