# Derivative, f(x) question

• Mar 20th 2012, 04:29 AM
Hooperoo
Derivative, f(x) question
hi friends

confused here. question is

f(x) = x / (x-1) use the definition of the derivative to determine f ' (x)

I know it has something to do with inverse functions but i dont know how to start.

thanks
• Mar 20th 2012, 04:42 AM
Plato
Re: Derivative, f(x) question
Quote:

Originally Posted by Hooperoo
f(x) = x / (x-1) use the definition of the derivative to determine f ' (x)
I know it has something to do with inverse functions but i dont know how to start.

As written, it has nothing to do with inverse.

You find ${\lim _{h \to 0}}\frac{{f(x + h) - f(x)}}{h}$
• Mar 20th 2012, 04:57 AM
princeps
Re: Derivative, f(x) question
Quote:

Originally Posted by Hooperoo
hi friends

confused here. question is

f(x) = x / (x-1) use the definition of the derivative to determine f ' (x)

I know it has something to do with inverse functions but i dont know how to start.

$\displaystyle \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}=\displaystyle \lim_{h \to 0}\frac{\frac{x+h}{x+h-1}-\frac{x}{x-1}}{h}=\displaystyle \lim_{h \to 0} \frac{-1}{(x+h-1)(x-1)}=\frac{-1}{(x-1)^2}$