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Derivative Using Dirac Delta Function
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)
In the previous portion I was able to prove
x \frac{d}{dx} (\delta(x))= -\delta(x)
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.
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.
