Diff, derivative does not exist

My code is:

fun=@(x) abs(x-1);
pfun=@(x) diff(fun(x),x);
feval(pfun,1)

It didn't return any answer after running the code. My general point, if we want to use Matlab to take the derivative of a function, but the derivative of this funtion does not exist everywhere (like the point 1 in fun(x)). How Matlab return the value? If there are infinite numbers of such points, how Matlab deal with this issue? Any help is very appreciated!

[madhan ravi]

Try the below (yet it is not clear what point you are trying to make):

syms x
fun=abs(x-1);
pfun(x)=diff(fun,x);
pfun(1) % evaluated at point 1

[James_111]

Thank you so much, Madhan! My point is, suppose you have a function, and you want to use Matlab to take the derivative of this function. However, the derivative may not exist everywhere. For example, like abs(x-1), the derivative at the point of 1 does not exist, as the left derivative is not equal to the right derivative. In this case, how could we still use diff? Interesting, like your code, it returns 0.

[Walter Roberson]

You are not doing a symbolic derivative. You are evaluating pfun(1) which is pfun with numeric input. You pass that numeric input to abs(x-1), getting a numeric output. Your diff() of a numeric input is finite differences, not derivative.

[James_111]

Thank you so much for pointing out the "finite difference", Walter!