Derivative of the Dirac Delta

1. Sep 1, 2008

CasualDays

Derivative Using Dirac Delta Function

1. The problem statement, all variables and given/known data
Let $$\theta$$(x) be the step function:

$$\theta$$(x) be equivalent to

1, if x > 0
0, if x $$\leq$$ 0

Show that $$\frac{d \theta }{dx}$$ = $$\delta$$(x)

2. Relevant equations
In the previous portion I was able to prove
x $$\frac{d}{dx}$$ ($$\delta$$(x))= -$$\delta$$(x)

3. The attempt at a solution
I thought the problem was a heavyside problem but upon closer inspection, I noticed that on the heavyside step function it is 1 when x $$\geq$$ 0.

So how do I resolve this? Is there a way to change it so that it looks like a heavyside function, because that makes the problem much more convenient.:rofl:

2. Sep 2, 2008

tiny-tim

Hi CasualDays!

(have a theta: θ and a delta: δ )

Hint: what is 1 - θ(x)?

3. Sep 2, 2008

CasualDays

It's always the easy solutions that allude me..

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