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.
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.
This solution provides some explanation for differentiability and function operation.