# Thread: Question on Definition of Derivative

1. ## Question on Definition of Derivative

I am evaluating the function f(x) = x / (x-1)

I set it up

lim h-> 0 x+h / (x+h+1) - x/(x-1)
----------------------
h

I am not sure how to simplify the top or if I set this up correctly. Thanks for the help!

2. Originally Posted by KarlosK
I am evaluating the function f(x) = x / (x-1)

I set it up

lim h-> 0 x+h / (x+h+1) - x/(x-1)
----------------------
h

I am not sure how to simplify the top or if I set this up correctly. Thanks for the help!

Either you take a peek at the "help with Latex" section to learn how to properly write maths or else add enough parentheses to make your mathematical expressions clear!

What has to be done is some basic algebraic manipulations which are very important to get along with maths:

$\displaystyle \lim_{h\to\ 0}\frac{\frac{x+h}{x+h-1}-\frac{x}{x-1}}{h}$ $\displaystyle =\lim_{h\to 0}\frac{\frac{(x+h)(x-1)-x(x+h-1)}{(x-1)(x+h-1)}}{h}$ $\displaystyle =\lim_{h\to 0} \frac{-h}{h(x-1)(x+h-1)}=\lim_{h\to 0}-\frac{1}{(x-1)(x+h-1)}=$ ...

Tonio