# Can someone explain how to prove this equality with respect to Dirac-Delta function?

I saw the following equations.

\begin{align} \delta(ax) &= \frac {1} {\lvert a \rvert} \delta(x)\\ \delta(x^2-a^2) &= \frac {1} {2\lvert a \rvert} \left [ {\delta(x+a) + \delta(x-a)} \right ] \end{align}

I think the equation below is the general expression. Can someone let me know how the equation below is induced?

$$\delta \left [ g(x) \right ]=\sum_i \frac { \delta(x-x_i) } { g'(x_i) }$$

Please don't use slang and abbreviations. I am not a native English speaker.