derivative of x/x-1-including h!!!

Hello!

Now, I have to count derivative from :

it would of course not be a problem IF the result would not be:

So, obviously it is the whole procedure including the proof of the rule for the derivative of the rational function and that is what I am asking about.

(Of course I am avare h is almost 0, but I am interested to the whoel procedure how didi they get it!)

I tried like this:

and got of course:

can someone help?

Did I make a mistake?

Many thanks!

Re: derivative of x/x-1-including h!!!

Quote:

Originally Posted by

**Boo** Hello!

Now, I have to count derivative from :

I tried like this:

and got of course:

You forgot that it is:

Re: derivative of x/x-1-including h!!!

O !

Thanks, Plato!!!

So, we obvioulsy get the rule for the derivative of the rational function out of it...

so:

Re: derivative of x/x-1-including h!!!

Quote:

Originally Posted by

**Boo** O !

Thanks, Plato!!!

So, we obvioulsy get the rule for the derivative of the rational function out of it...

so:

WHAT? What is the limit as h goes to 0?

Re: derivative of x/x-1-including h!!!

Quote:

Originally Posted by

**Boo** Hello!

Now, I have to count derivative from :

it would of course not be a problem IF the result would not be:

So, obviously it is the whole procedure including the proof of the rule for the derivative of the rational function and that is what I am asking about.

(Of course I am avare h is almost 0, but I am interested to the whoel procedure how didi they get it!)

I tried like this:

and got of course:

can someone help?

Did I make a mistake?

Many thanks!

A first principles approach for this problem may be easier if you can see that .