Is a unit doublet function an even function or odd function?

Dirac’s delta function is defined by the following property 

δ(t) = 0 at t !=0

           ∞ at t=0.

The derivative of an even function is an odd function and derivative of an odd function is even function .

ex, f(x)=x^5

so this is an odd function because f(-x)=-f(x).

Now if we apply derivative on the f(x) then it becomes f’(x)=x^4 and f’(x) is an even function. further we differentiate the function then it becomes f’’(x)=x^3 and it is an odd function and so on .

Doublet function is the 1st derivative of impulse function[delta(-t)=delta(t)]

Therefore derivative of delta function is an odd function.