The derivative - why does differentiation work?

[mardat]

Think of the function f(x) = 1/x. It's value is never actually 0, however as x approaches infinity, f(x) does approach 0. When you're finding the derivative of something, the principle is similar - you're finding what value the gradient is approaching as the distance between the two points you pick approaches 0 (as the value of h approaches 0). In the case of differentiation, the gradient at that point will actually be whatever it is approaching.

[paulsterio]

For those of you who do MUEP/UMEP maths or are in university, you'll probably know this, its probably too advanced for high school level, but its basically a way of understanding limits better

You know how basically when you find a limit, you're usually taught to "sub it in" and that will give you the value of the limit, this actually works because of a concept known as the "epsilon-delta proof"

This basically states that as we restrict x to being within delta units of what we are approaching, then because of that restriction, f(x) becomes restricted to being within epsilon units of L.

Basically all your Limit Theorems are based on Epsilon Delta proofs, also, for now, i'd say just accept the concept of a derivative, once you reach applications of differentiation, you'll understand a lot more, if now, you could always try reading Pre-Calculus or Calculus I books from uni, which might explain it better (: - high school maths tends to simplify things a bit (:

[azn_dj]

Lucky thing is, it is very rare that you have to use the "first principles" to find the derivatives. We have magical formulas that help us do it for us But that is what you're actually doing when you find a derivative.

(You dont really need to understand that it works even. You just need to know it works and then use the formula )

Noooo! I must know!

Hence my long winded explanation

[abeybaby]

@paulsterio
i wanna know why you know about epsilon delta proofs! arent you in yr 12?

[paulsterio]

@paulsterio
i wanna know why you know about epsilon delta proofs! arent you in yr 12?

haha, i just like to read, and i consider myself quite interested in maths so like internet...etc
and yeshh i'm in year 12