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Differentiation of composite function - integral form

(See attached file for full problem description with proper symbols)

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Assume that f is continuous on [a,b], g is differentiable on [c,d], g([c,d]) [a,b] and

F(x) =
For each x [c,d].

Prove that
F'(x)=f(g(x))g'(x)
For each x (c,d).

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Solution Preview

Given that f is continuous on [a,b], it follows that
dF = dg * f(g) ...

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