# problems regarding differentiability and function operation

Please provide detailed solution:

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.

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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