Question

This is a CALCULUS question, "Derivatives As A function"

Answer 1

Derivative Functions

The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. We can formally define a derivative function as follows.

Definition:

let f be a function. The derivative function, denoted by f', is the function whose domain consists of those values of  x  such that the following limit exists:

$f'(x)= \lim_\\ \ \\ \frac{f(x+h)-f(x)}{h} {h \to 0}$