/sci/, I'm trying to recall some basic facts here. What

I have no idea what I am reading here. Clearly the derivative does not exist.

>>8636849
the weak derivative exists, and is equal to 5*delta(x-1)

>>8636852
Is there a proof of this basic property? The delta(x-1) makes sense to me, but it's not clear why the coefficient is five and not just one.

>>8636862
Because it goes from y=0 to y=5

>>8636862
let H(x) be the function in the OP

the weak derivative is by definition the function that makes the integration by parts formula true

so you need to check that

[math] \int_{-\infty}^{\infty}H(x)f'(x)dx=-\int_{\infty}^{\infty} 5\delta(x-1)f(x)dx[/math]

for every function f with the property that f(x)=0 for all |x| sufficiently large

>>8637015
typo: right hand integral should go from negative infinity to positive infinity