What is the limit definition of the derivative of the function $y=f(x)$ ?

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Answer 1 · 2018-03-11T17:51:12

There are several ways of writing it. They all capture the same idea.

For $y=f(x)$ , the derivative of $y$ (with respect to $x$ ) is

$y' = dy/dx = lim_(Deltax rarr0) (Delta y)/(Delta x)$

$f'(x) = lim_(Deltax rarr0) (f(x+Delta x)-f(x))/(Delta x)$

$f'(x) = lim_(hrarr0) (f(x+h)-f(x))/(h)$

$f'(x) = lim_(urarrx) (f(u)-f(x))/(u-x)$

What is the limit definition of the derivative of the function y=f(x)y=f(x) ?