Is the Derivative of an Inverse Function Valid? Insights and Links!

[Petrus]

Hello MHB,
I am aware of there is two way, u can use chain rule or defination of derivate. I totally understand the proof with this type Derivative of Inverse Function but is that a valid proof? How ever our teacher did proof this with derivate defination which I don't understand from my textbook. What is your thought? Any good link that explain this proof with derivate defination

I am aware that we use chain rule and I am training for oral exam and I guess I will have to proof this chain rule in this one.

edit: why should $$f'(x) \neq 0$$ should it be $$f'(y) \neq 0$$
Regards,
$$|\pi\rangle$$

 

[I like Serena]

re: proof of inverse derivative

Hello MHB,
I am aware of there is two way, u can use chain rule or defination of derivate. I totally understand the proof with this type Derivative of Inverse Function but is that a valid proof? How ever our teacher did proof this with derivate defination which I don't understand from my textbook. What is your thought? Any good link that explain this proof with derivate defination

I am aware that we use chain rule and I am training for oral exam and I guess I will have to proof this chain rule in this one.

edit: why should $$f'(x) \neq 0$$ should it be $$f'(y) \neq 0$$
Regards,
$$|\pi\rangle$$

That proof looks valid to me.

Note that there may be some confusion about x and y, since their meanings are swapped around after the first line.
In the first line x is used as the argument of f, but in the second line and thereafter x is used as the argument of $f^{-1}$ instead (where you might expect y to be the argument).

 

[Petrus]

Re: proof of inverse derivative

That proof looks valid to me.

Note that there may be some confusion about x and y, since their meanings are swapped around after the first line.
In the first line x is used as the argument of f, but in the second line and thereafter x is used as the argument of $f^{-1}$ instead (where you might expect y to be the argument).

Thanks for taking your time I like Serena!:)

PS. Should I be rational or real:p

Regards,
$$|\pi\rangle$$

 

[I like Serena]

Re: proof of inverse derivative

Thanks for taking your time I like Serena!:)

PS. Should I be rational or real:p

Regards,
$$|\pi\rangle$$

I think that $$|\pi\rangle$$ is imaginary. (Pizza)