# Every Absolutely continuous function is of bounded variation and hence is differentiable almost everywhere.

I was trying to prove this theorem-

"Every Absolutely continuous function is of bounded variation and hence is differentiable almost everywhere."

I got the first part like how Absolutely continuous function is of bounded variation but I am struggling to prove that if it of bounded variation then it is differentiable almost everywhere.

I tried to connect the fact that

$1)$ A function of bounded variation can be written as the difference of two increasing functions.

$2)$ A function $f:[a,b] \rightarrow \mathbb{R}$ be a monotone function then $f$ is differentiable almost everywhere.

But it is not working as difference of two increasing functions need not be a monotone function.

So how do I prove that a function of bounded variation implies it is differentiable almost everywhere?

Am I missing something?

Any help is great.