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    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).

    © BrainMass Inc. brainmass.com December 15, 2022, 5:29 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/differentiation-composite-function-integral-form-86718

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

    Solution Summary

    Differentiation of composite functions and integral forms are determined.

    $2.49

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