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    problems regarding differentiability and function operation

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    What can you say about the differentiability of fg at x = c in each of the following cases? (Here the function fg is defined by fg(x) = f(x)g(x)).
    (a) f is differentiable at c, but g is not.
    (b) f is not differentiable at c, and neither is g.
    (c) both f and g are differentiable at c.

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    https://brainmass.com/math/graphs-and-functions/problems-regarding-differentiability-function-operation-460525

    Solution Preview

    Hi there,

    Thanks for letting me work on your questions. When c condition is met, (fg(x))'=f(x)'g(x)=f(x)g(x)'. so fg(x) is differentiable.
    However, for condition a and b, the answer is not conclusive.
    For ...

    Solution Summary

    This solution provides some explanation for differentiability and function operation.

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