Exploring the Relationship between the Step Function and Dirac Delta Function

[CasualDays]

Derivative Using Dirac Delta Function

Homework Statement

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)

Homework Equations

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

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.

 

[tiny-tim]

Hi CasualDays!

(have a theta: θ and a delta: δ )

Hint: what is 1 - θ(x)?

 

[CasualDays]

Hi CasualDays!

(have a theta: θ and a delta: δ )

Hint: what is 1 - θ(x)?

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