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# Why does diffrentiation work the way it does?

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1. When you diffrentiate 2x2 Why do we get 4x as the diffrential?

Why does the method work? I was just curious.

NOTE: I am not asking how we diffrentiate. I want to know why it works.
2. (Original post by SirRaza97)
When you diffrentiate 2x2 Why do we get 4x as the diffrential?

Why does the method work? I was just curious.

NOTE: I am not asking how we diffrentiate. I want to know why it works.
https://en.wikipedia.org/wiki/Derivative
3. (Original post by SirRaza97)
When you diffrentiate 2x2 Why do we get 4x as the diffrential?

Why does the method work? I was just curious.

NOTE: I am not asking how we diffrentiate. I want to know why it works.
4. Anything but Wikipedia?
5. (Original post by SirRaza97)
Anything but Wikipedia?
It's explained clearly.
6. (Original post by SirRaza97)
When you diffrentiate 2x2 Why do we get 4x as the diffrential?

Why does the method work? I was just curious.

NOTE: I am not asking how we diffrentiate. I want to know why it works.
Broadly, because of the binomial expansion theorem:

When you expand out with the binomial theorem, the only term that survives is the term
Spoiler:
Show

Another method of showing this is using the definition of as "the function that equals it's own derivative. That's perfectly self contained a definition, and you then then say:

However, that requires you to know something about: log laws, the chain rule, inverse functions/implicit differentiation. Some of that stuff is C3, wherease the binomial expansion theorem is taught in C2.
7. (Original post by SirRaza97)
Anything but Wikipedia?
8. (Original post by lerjj)
Broadly, because of the binomial expansion theorem:

When you expand out with the binomial theorem, the only term that survives is the term
What do you mean by survives?

We have .
9. (Original post by SirRaza97)
When you diffrentiate 2x2 Why do we get 4x as the diffrential?

Why does the method work? I was just curious.

NOTE: I am not asking how we diffrentiate. I want to know why it works.
I recommend you watch this video:

10. (Original post by Zacken)
What do you mean by survives?

We have .
Sorry, by "survive" I mean that in the limit that's the only term that doesn't vanish (after dividing by h in every term, of course).
11. (Original post by lerjj)
Sorry, by "survive" I mean that in the limit that's the only term that doesn't vanish (after dividing by h in every term, of course).
Ah, okay - I wasn't sure because you left an in your answer so was wondering whether you'd taken the limit or not yet. S'alright now, thanks.

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