The limit definition of the derivative produces a value for each x at which the derivative is defined, and this leads to a new function whose formula is y = f'(x). Hence we talk both about a given fun...The limit definition of the derivative produces a value for each x at which the derivative is defined, and this leads to a new function whose formula is y = f'(x). Hence we talk both about a given function f and its derivative f'. It is especially important to note that taking the derivative is a process that starts with a given function (f) and produces a new, related function (f').
