# When was the derivative of sin(X) first determined ?

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I want to know in the timeline of mathematics , considering what was considered as far as had been discovered at that time , where I place ?

For example, if you can calculate a derivative from first principles you are at the same point Newton was when he discovered calculus.

Am I still at that point in time ? I assume so. So I have the same knowledge that the best mathematicians of the 17th century had !

For example, if you can calculate a derivative from first principles you are at the same point Newton was when he discovered calculus.

Am I still at that point in time ? I assume so. So I have the same knowledge that the best mathematicians of the 17th century had !

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#2

(Original post by

I want to know in the timeline of mathematics , considering what was considered as far as had been discovered at that time , where I place ?

For example, if you can calculate a derivative from first principles youu are at the same point Newton was when he discovered calculus.

Am I still at that point in time ? I assume so. So I have the same knowledge that the best mathematicians of the 17th century had !

**seals2001**)I want to know in the timeline of mathematics , considering what was considered as far as had been discovered at that time , where I place ?

For example, if you can calculate a derivative from first principles youu are at the same point Newton was when he discovered calculus.

Am I still at that point in time ? I assume so. So I have the same knowledge that the best mathematicians of the 17th century had !

Have a read of a good maths history book, Newton did a fair bit more than that and others had been kicking around ideas about calculus for 50-100 years before, but he unified the approach and applied it to understand gravity/elliptical motion, amongst other things.

Last edited by mqb2766; 3 weeks ago

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#3

(Original post by

Errr can you differentiate sin() from first principles?

**mqb2766**)Errr can you differentiate sin() from first principles?

Then, let so and and so:

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#4

(Original post by

Errr can you differentiate sin() from first principles?

**mqb2766**)Errr can you differentiate sin() from first principles?

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#6

(Original post by

Care to elaborate?

**lordaxil**)Care to elaborate?

Edit: FWIW, it's a little less obvious but if you use the trig sum<->product formulas you can show , which reduces the "limit type" results you need to just .

Last edited by DFranklin; 3 weeks ago

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#7

(Original post by

Care to elaborate?

**lordaxil**)Care to elaborate?

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#8

(Original post by

isn't a meaningfull statement when talking about limits. You can't pick and choose which bits of the limit you move outside. If I give you the benefit of the doubt about , it's still a result claimed without proof. Same for . In addition, isn't enough to deduce the result you want.

**DFranklin**)isn't a meaningfull statement when talking about limits. You can't pick and choose which bits of the limit you move outside. If I give you the benefit of the doubt about , it's still a result claimed without proof. Same for . In addition, isn't enough to deduce the result you want.

(Original post by

Edit: FWIW, it's a little less obvious but if you use the trig sum<->product formulas you can show , which reduces the "limit type" results you need to just .

**DFranklin**)Edit: FWIW, it's a little less obvious but if you use the trig sum<->product formulas you can show , which reduces the "limit type" results you need to just .

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(Original post by

isn't a meaningfull statement when talking about limits. You can't pick and choose which bits of the limit you move outside. If I give you the benefit of the doubt about , it's still a result claimed without proof. Same for . In addition, isn't enough to deduce the result you want.

Edit: FWIW, it's a little less obvious but if you use the trig sum<->product formulas you can show , which reduces the "limit type" results you need to just .

**DFranklin**)isn't a meaningfull statement when talking about limits. You can't pick and choose which bits of the limit you move outside. If I give you the benefit of the doubt about , it's still a result claimed without proof. Same for . In addition, isn't enough to deduce the result you want.

Edit: FWIW, it's a little less obvious but if you use the trig sum<->product formulas you can show , which reduces the "limit type" results you need to just .

Thanks.

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#10

(Original post by

Clearly, those limiting behaviours only apply as . A proof for either result can be obtained without resort to calculus.

**lordaxil**)Clearly, those limiting behaviours only apply as . A proof for either result can be obtained without resort to calculus.

**don't**then I really don't know what you mean).

More fundamentally, you can't (always) look at a limiting expression and say "I'll take the limits for those bits out of the limit, but I'll leave some other bits in".

In your limit you've claimed that by observing that .

This is not a valid arguement. If we rearrange slightly as: we see that you are dividing by .

So the mere knowledge that is insufficient; you need instead , which is a much stronger statement..

More elegant, no doubt, but the gain in rigour comes at loss of clarity.

**how quickly**is worth it, IMNSHO.

Last edited by DFranklin; 3 weeks ago

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#11

(Original post by

I'm not nitpicking about whether you explicitly say "as "; it's clear enough from context. But my question is: what is even supposed to mean? If you mean , you should say so (and if you

**DFranklin**)I'm not nitpicking about whether you explicitly say "as "; it's clear enough from context. But my question is: what is even supposed to mean? If you mean , you should say so (and if you

**don't**then I really don't know what you mean).
(Original post by

More fundamentally, you can't (always) look at a limiting expression and say "I'll take the limits for those bits out of the limit, but I'll leave some other bits in".

**DFranklin**)More fundamentally, you can't (always) look at a limiting expression and say "I'll take the limits for those bits out of the limit, but I'll leave some other bits in".

(Original post by

Not much point in a "proof" that's clear but wrong. Rearranging to avoid the need of results on

**DFranklin**)Not much point in a "proof" that's clear but wrong. Rearranging to avoid the need of results on

**how quickly**is worth it, IMNSHO.
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#12

(Original post by

Yes, that's what I mean. As you say, it couldn't really mean anything else.

Fair point. In this case, it is OK to do though.

**lordaxil**)Yes, that's what I mean. As you say, it couldn't really mean anything else.

Fair point. In this case, it is OK to do though.

I wasn't aiming for full mathematical rigour - just to show that sin(x) can be differentiated from first principles, which you have agreed with me is possible.

Last edited by DFranklin; 3 weeks ago

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#13

Yes, you are right. What I wrote originally was wrong and I see that now. Correction repped.

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