Hello everyone,

I would like some help on proving the following statement:

Let $f\in\mathrm{BV}[a,b]$, i.e. $f$ is of bounded variation and let $T(x)$ be the total variation of $f$ on $[a,x]$ for $x\in[a,b]$, then the derivative of $T$ is equal to the derivative of $|f|$ a.e. that is, $$T'= |f|' \quad\mathrm{almost\;everywhere}.$$

Any help is appreciated.