Derivative - Wikipedia
https://en.wikipedia.org/wiki/DerivativeRelative to a hyperreal extension R ⊂ R of the real numbers, the derivative of a real function y = f(x) at a real point x can be defined as the shadow of the quotient ∆y/∆x for infinitesimal ∆x, where ∆y = f(x + ∆x) − f(x). Here the natural extension of f to the hyperreals is still denoted f. Here the derivative is said to exist if the shadow is independent of the infinitesimal chosen.
Definition of derivative
web.iit.edu › pdfs › what_are_DerivativeDefinition of Derivative •As we saw, as the change in x is made smaller and smaller, the value of the quotient – often called the Difference Quotient – comes closer and closer to 4. •The formal way of writing it is • ′2=lim ℎ→0 𝑓2+ℎ−𝑓(2) ℎ =4 •Think of the variable h as a “slider”. You