What is the derivative of $u(x)=\delta (x-y)H(y)$ wih respect to x and y? Thanks
2026-03-28 09:45:38.1774691138
Derivative of $\delta (x-a)$
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It's $\delta'(x-a)$. This is the distribution such that $$\int \delta'(x-a) \, \varphi(x) \, dx = - \int \delta(x-a) \ \varphi'(x) \, dx = - \varphi'(a)$$ for every test function $\varphi.$