Prove the product rule for derivatives. Fuck your book, just type it here
------->

On Thursday, October 19, 2023 at 5:10:32 PM UTC-7, Mathin3D wrote:
> Prove the product rule for derivatives. Fuck your book, just type it here
> ------->

You see what you do is take the x + delta x and delta x, going to zero,
anyways you multiply out those terms together their powers, then
reduce along down terms, then again as reducing, demonstrating
one way power rule reducing for derivatives occurs, for "not for -1".

Then, "-1" is the case, that the anti-derivative of x^ -1, doesn't exist
like the others, though that it gets into lnx and x (lnx -1) or as so on,
the power rule considered to be defined according to powers being
defined as b ^ p/r, being to the p'th power, to the r'th root.

Anyways I was just reading Courant while I've been studying the
anti-derivative of x=y and y = 1/x, Courant fills in "not for -1", after
writing up powers and roots as fractional powers, and writing a quick
derivation of the power rule, showing it's from the products of the
vanishing terms, algebraically as they align, according their systems
of units.

I.e., it's like demonstrating with the h + delta h, or as h goes to 0,
x or h, demonstrating the fundamental derivative, according to delta h
being a small quantity that dh/dh = 1, but dh going to zero. The power
rule just cranks out the products of those then reduces and demonstrates
similarly as Courant does it.

Not for -1, ....

All is fine, except you are not crackpot John Gabriel and you did not use his buIIsh t theories. Reading titles can be helpful!

On Thursday, October 19, 2023 at 11:12:24 PM UTC-4, Ross Finlayson wrote:
> On Thursday, October 19, 2023 at 5:10:32 PM UTC-7, Mathin3D wrote:
> > Prove the product rule for derivatives. Fuck your book, just type it here
> > ------->
> You see what you do is take the x + delta x and delta x, going to zero,
> anyways you multiply out those terms together their powers, then
> reduce along down terms, then again as reducing, demonstrating
> one way power rule reducing for derivatives occurs, for "not for -1".
>
> Then, "-1" is the case, that the anti-derivative of x^ -1, doesn't exist
> like the others, though that it gets into lnx and x (lnx -1) or as so on,
> the power rule considered to be defined according to powers being
> defined as b ^ p/r, being to the p'th power, to the r'th root.
>
> Anyways I was just reading Courant while I've been studying the
> anti-derivative of x=y and y = 1/x, Courant fills in "not for -1", after
> writing up powers and roots as fractional powers, and writing a quick
> derivation of the power rule, showing it's from the products of the
> vanishing terms, algebraically as they align, according their systems
> of units.
>
> I.e., it's like demonstrating with the h + delta h, or as h goes to 0,
> x or h, demonstrating the fundamental derivative, according to delta h
> being a small quantity that dh/dh = 1, but dh going to zero. The power
> rule just cranks out the products of those then reduces and demonstrates
> similarly as Courant does it.
>
> Not for -1, ....