Derivative of Dirac Delta - Fourier Transform - Time Differentitation Property

[p75213]

Homework Statement

I am using the time differentiation property to find the Fourier transform of the following function:

Homework Equations

f(t)=2r(t)-2r(t-1)-2u(t-2)

The Attempt at a Solution

f'(t)=2u(t)-2u(t-1)-2δ(t-2)
f''(t)=2δ(t)-2δ(t-1)-??

Can somebody explain what the derivative of the dirac delta function is?

 

[gabbagabbahey]

The easiest way to see what $\frac{d}{dx}\delta(x)$ is, is to multiply it by a simple test function like $x$ and Integrate over any interval enclosing the origin, using integration by parts.