Ex. 6.1

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differentiability of composite functions

Surb (https://math.stackexchange.com/users/154545/surb), Differentiability of product/composition of function, URL (version: 2017-04-13): https://math.stackexchange.com/q/856415 user147263, Can it be that $f$ and $g$ are everywhere continuous but nowhere differentiable but that $f \circ g$ is differentiable?, URL (version: 2017-04-13): https://math.stackexchange.com/q/1643859

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differentiability of product (sum) of functions

martini (https://math.stackexchange.com/users/15379/martini), Can we always multiply some function that is not differentiable everywhere with function that is to obtain differentiable product?, URL (version: 2015-12-04): https://math.stackexchange.com/q/1559702 Hagen von Eitzen (https://math.stackexchange.com/users/39174/hagen-von-eitzen), Is 'a' differentiable in f when f is a product of a differentiable and non-differentiable function?, URL (version: 2015-07-03): https://math.stackexchange.com/q/1348081 Silvia Ghinassi (https://math.stackexchange.com/users/258310/silvia-ghinassi), Two non-differentiable functions whose product is differentiable., URL (version: 2015-11-14): https://math.stackexchange.com/q/1528901 the Exercise 5.2.2 mentioned in the comment is based on the above discussion, we know that (c) is impossible.