# Help me solving a Derivation equation

1. Mar 8, 2014

1. The problem statement, all variables and given/known data
find the derivative of the given function:

f(x)= 6 - (1/x) / x-2

2. Relevant equations

3. The attempt at a solution
the solution on the answer key is (-6x^2 + 2x - 2 ) / (x^2 (x-2)^2)

i don't know how to solve it :(

2. Mar 8, 2014

### Simon Bridge

Welcome to PF;
Lets just check that I understand you:

You are given $$f(x)=\frac{6-\frac{1}{x}}{x-2}$$... and you are asked to find $$f^\prime (x)=\cdots$$

It looks awkward - have you tried expressing the fraction in a simpler form?
There is a rule for differentiations where f(x) takes the form: $$f(x)=\frac{g(x)}{h(x)}$$ ... do you know what that is?

3. Mar 8, 2014

### SammyS

Staff Emeritus
Assuming that Simon correctly interpreted what your function should have actually been, you needed to include sufficient parentheses .

f(x) = (6 - (1/x) ) / (x-2)

Last edited: Mar 8, 2014
4. Mar 8, 2014

### Ray Vickson

You have written
$$f(x) = 6 - \frac{1}{x x} - 2 = 4 - \frac{1}{x^2}$$
This is what I get when I read your expression using standard parsing rules for mathematical expressions.
If you mean hte above then you do not need to change anything. However, if you mean
$$f(x) = 6 - \frac{1}{x(x-2)}$$
then you need parentheses, like this: f(x) = 6 - 1/(x(x-2)). If you mean
$$f(x) = \frac{6 - (1/x)}{x} - 2$$
then you need parentheses, like this: f(x) = (6 - (1/x))/x - 2. Finally, if you mean
$$f(x) = \frac{6 - (1/x)}{x-2}$$
then use parentheses like this: f(x) = (6 - (1/x))/(x-2).

5. Mar 8, 2014

### Simon Bridge

Well, considering that: $$\frac{d}{dx}\frac{6-\frac{1}{x}}{x-2}= \frac{-6x^2 + 2x - 2}{x^2(x-2)^2}$$... it's probably a good guess ;)

What is needed now is a follow up from you.
It is tricky to guide you through this one without effectively providing the answer so I want to know where you are stuck. Please show us your best attempt.

6. Mar 9, 2014