What the heck's the point of this..

[kenhung123]

Essentials went into the effort to rearrange the chain rule and derive this formula: dy/dx=1/(dx/dy)
Then they did

This apparently is used when the power is a fraction..I have no idea why they bothered to show this?

I have attached the page reference..

[TrueTears]

an application

x = siny find dy/dx

thus there is a point

[/0]

They started only with the chain rule and the knowledge that differentiation works for whole number powers, and they used them together to prove that it also works for fractional powers.

You see, if you start with those assumptions you can't just immediately differentiate , you have to do what they did, differentiate


The reason why they showed you this is, I presume, to simply give you an intuitive understanding of why fractional powers work too.


(As truetears mentioned, this technique is also used in other places)

[kenhung123]

Thank you TT and /0.
Is it necessary to learn the proofs for the different rules?

[/0]

You won't need to know the proofs for the differentiation rules.

[kenhung123]

Hmm I think they were trying to extend the power rule as we were introduced to use it for only integer powers and they want to prove that it works for fractional powers too