What is the product of Dirac Delta function and $t$? [closed]

1. What is the derivative of Dirac delta function?
2. What will be the value of delta function at t 0?
3. What are the properties of Dirac delta function?

What is the derivative of Dirac delta function?

In the theory of electromagnetism, the first derivative of the delta function represents a point magnetic dipole situated at the origin. Accordingly, it is referred to as a dipole or the doublet function.

What will be the value of delta function at t 0?

So my understanding is that a delta function δ(t) has the value of ∞ at t=0 and δ(t)=0 everywhere else.

What are the properties of Dirac delta function?

6.3 Properties of the Dirac Delta Function

where a=constant and g(xi)=0, g ( x i ) = 0 , g′(xi)≠0. g ′ ( x i ) ≠ 0 . The first two properties show that the delta function is even and its derivative is odd.