# Differentiation of composite function - integral form

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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 Summary

Differentiation of composite functions and integral forms are determined.

##### Solution Preview

Given that f is continuous on [a,b], it follows that

dF = dg * f(g) ...

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