Help me solving a Derivation equation

[ishahad]

Homework Statement

find the derivative of the given function:

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

Homework Equations

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 :(

 

[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?

 

[SammyS]

Homework Statement

find the derivative of the given function:

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

Homework Equations

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 :(

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)

 

[Ray Vickson]

Homework Statement

find the derivative of the given function:

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

Homework Equations

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 :(

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).

 

[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 ;)

@ishahad:
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.

 

[Mark44]

Please, no more help, hints, or guidance until ishahad returns.