Question

Are there any functions which are unable to be differentiated?

As in, say I had a function `f(x)`, and the derivative `f'(x)`. Is there any function for `f(x)` where the equation for `f'(x)` cannot be worked out using any differentiation rules and instead have to be done graphically.

Answer 1

Perhaps this is the kind of thing you're wondering about.

Explanation:

`f(x)={(x^2sin(1/x), "if", x != 0) ,(0,"if",x = 0):}`.

`f` can be differentiated by the chain rule at all `x != 0`, but to show that `f'(0)=0` we use (need?) the definition of derivative.

Graphical techniques are only as accurate as our ability to graph and read the graph.