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5:38 It’s interesting that you’ve never seen this long-division-based method for finding derivatives when it was the original way that Newton performed it, as seen in his Method of Fluxions. He found many infinite series and derivatives with long division of polynomials, you should look into it
yes! make video on finite element methods, finite difference methods, calculus, slve pipe problems, civil engineering! I can see the transition into real math ;)
I argue that they are equal. you just treat them as different variables before stating their equality. Derivative is the instantaneous slope at a point, meaning that if x and c are not equal, it's not differentiation.
Yes, but the prompt specifically said to use the method he used. The fact that he got the right answer can be verified with the power rule. But ... why does the power rule work? Can you prove it?
@@tedforringer9124 I can prove it. There is also a nice explanation on 3Blue1Brown’s channel. This is probably one of the first things you learn in calculus, so I was just slightly underwhelmed (even though I did expect it) when the answer was 5x^4. Hence I wrote this comment. And yes, I do know what the question asked, and what its specifications were. This video was disguised as a proof of the power rule using the definition of a derivative. Nonetheless, it was still pretty cool.
I watch these, but I don't understand any of it. How exciting!
Hang in there. Go to the earlier stuff and build it up. You will have to attempt some problems yourself though.
This is Calc 1. You'll make it up to this level some day!
Great job, Andy! ❤ this channel. I wish my teachers had been as good as you when I was in school.
This guy makes me feel like I know how to do this even though I don't. Good teacher.
I remember i first learned this in physics on topic about instantaneous velocity and speed
But idk what is that anymore😂😂
5:38 It’s interesting that you’ve never seen this long-division-based method for finding derivatives when it was the original way that Newton performed it, as seen in his Method of Fluxions. He found many infinite series and derivatives with long division of polynomials, you should look into it
At 5:43 Brilliant segue.
How exciting!
Important! Save.
That was truly exciting! Nice work, Andy.
I didn't get any of it either. 🤪
yes! make video on finite element methods, finite difference methods, calculus, slve pipe problems, civil engineering!
I can see the transition into real math ;)
Isn't the slope formula
(y₂-y₁)÷(x₂-y₁)
Superbb!!!
Can't you do this with synthetic division? Just treat c as a constant and divide it. But, I guess long division also works
Until x is equal to c?? I think you mean “until x is really really really close to c to the point that x and c are virtually equal with each other”!!
until the difference between x and c is the same as the difference between 0.9... and 1
I argue that they are equal. you just treat them as different variables before stating their equality. Derivative is the instantaneous slope at a point, meaning that if x and c are not equal, it's not differentiation.
how exciting
Hi andy
New sub here 😮
Why didn't you use Ruffini's method to do this division? You would have solved it in a third of the time, maybe even less.
Hi
I used to know math ;)
hey
Basically the long version of chain rule
isn't this the power rule?
@@Ar-pz4cp it is i think
You should learn about the so-called "basic" more.
power rule?
Yes, but the prompt specifically said to use the method he used. The fact that he got the right answer can be verified with the power rule. But ... why does the power rule work? Can you prove it?
@@tedforringer9124 I can prove it. There is also a nice explanation on 3Blue1Brown’s channel. This is probably one of the first things you learn in calculus, so I was just slightly underwhelmed (even though I did expect it) when the answer was 5x^4. Hence I wrote this comment. And yes, I do know what the question asked, and what its specifications were. This video was disguised as a proof of the power rule using the definition of a derivative. Nonetheless, it was still pretty cool.
@@tedforringer9124The product rule and induction will prove the power rule for rational exponents.
This looks like stuff Newton did
First