Absolute continuity, another question,

I have another question on Absolute continuity :

Let f : [a,b] ---> R be a strictly increasing absolutely continuous function
and g : [f(a),f(b)] ---> R be an absolutely continuous function. I am trying
to prove that (g(f(x))) ' = g ' (f(x)) f ' (x) a.e. in [a,b], where g '
(f(x)) f ' (x) is understood to be 0 if f ' (x) = 0, regardless of whether
or not g ' (f(x)) exists.

I have shown that g o f is absolutely continuous (using monotonicity of f).
I tried to then represent g o f as the integral of its derivative, but I
couldn't see how this would lead me to what I need to prove.

Any ideas/help is appreciated,

James


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