>>13741132>it can't even be interpreted as a fraction (unlike regular derivatives)!Yes it can, go read Keisler:
https://people.math.wisc.edu/~keisler/calc.html>>13742962Not OP but you can read the first chapter of Keisler's book that i linked above if you really want to understand more, if you don't know infinitesimals then the closest intuition you can get is the following:
Let df = f(x_0) - f(x)
And let dx = x_0 - x
where x_0 is constant
Then the derivative at x_0 is df/dx as dx goes to 0, this is equivalent to the formal definition of the derivative.
