# Thread: definition of a derivative

1. ## definition of a derivative

I saw somewhere an alternative definition of a derivative.. It's basically the same when calculating but when looking at the graph- well, it'd only be right if the function was in some way simetrical. Am I right? Or does this work for any function..

What I'm trying to say.. d(x1,x2) is not equal to 2d(x,x1) in any given function.?
( h's are not the same in x1, x2)

definition: (you have 3 points here instead of 2)

x
x1 = x+h
x2 = x-h

$\displaystyle f'(x) = \lim_{h\to0} \frac {f(x+h) - f(x-h)}{2h}$

2. Originally Posted by metlx
I saw somewhere an alternative definition of a derivative.. It's basically the same when calculating but when looking at the graph- well, it'd only be right if the function was in some way simetrical. Am I right? Or does this work for any function..

$\displaystyle f'(x) = \lim_{h\to0} \frac {f(x+h) - f(x)}{h}$
Thought I'd correct that for you.

You can use this definition to take the derivative of absolutely anything, and can even use it to prove such things as the Chain Rule, Product Rule, Quotient Rule, derivatives of trigonometric function, etc.

However, this method, while it works, is extremely tedious. It's one of the most common complaints about it in the Calculus I classes at the college I'm currently attending.