If f is a function defined by the fomula f(x)=xe^(modx), then show that f is differentiable at every point c, with(adsbygoogle = window.adsbygoogle || []).push({});

f'(c)=(mod(c) +1)e^(modx)

The hint that is given is 'consider separately the cases cgreater than 0, c less than 0 and c=0

To prove that f is differemtiable at every point c, do I have to have f as 2 seorate functions mmultiplied together, and if each of them is differentiable then does it mean that f is differentiable? I tried this and it was fimne fpr the function equal to x, but I couldn't work it out for the function equal to e^(modx) . Is there a better way of proving that it is differentiable?

Also, is there a reason why we have mod(c) inside the brakcets of f'(c) as opposed to just c?

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# How to tell if a function is differentiable or not

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