Introduction to Electrodynamics · Problem 1.46

Vector Analysis — David J. Griffiths

Physics · dirac-delta-function

Problem

(a) Show that

x \frac{d}{dx}(\delta(x)) = -\delta(x).

[Hint: Use integration by parts.] (b) Let

\theta(x)

be the step function:

\theta(x) \equiv \begin{cases} 1, & \text{if } x > 0 \\ 0, & \text{if } x \le 0 \end{cases}.

Show that

d\theta/dx = \delta(x)