Originally Posted by

**Boo** Hello!

Now, I have to count derivative from :

$\displaystyle (\frac{x}{x-1}$

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

$\displaystyle -\frac{1}{(x-1)(x-1+h)}$

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:

$\displaystyle = \frac{x+h}{x+h-1}-\frac{x}{x-1}$

and got of course:

$\displaystyle =\frac{(x-1)(x+h)-x(x+h-1)}{(x+h-1)(x-1)}= \frac{-h}{(x+h-1)(x-1)}$

can someone help?

Did I make a mistake?

Many thanks!