# What is a derivative in the distribution sense?

1. Aug 15, 2015

### pellman

Never mind. I got this one. Couldn't figure out how to delete the post though.

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Last edited: Aug 15, 2015
2. Aug 15, 2015

### micromass

Let $u\in L^2(\mathbb{R})$ be a function such that for all smooth $\psi\in \mathcal{C}_c^1(\mathbb{R})$, we have that
$$\int_{-\infty}^{+\infty} \psi(x) u(x)dx = -\int_{-\infty}^{+\infty} \psi'(x) \varphi(x)dx$$
Then $u$ is said to be the derivative of $\varphi$ in the distributional sense.

3. Aug 15, 2015

### pellman

Thanks, micromass! I had just found the answer and was editing the OP. Still much appreciated though.