Help me solving a Derivation equation

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    Derivation
In summary: We can't do the work for them. In summary, the conversation was about finding the derivative of a given function, which involved simplifying and using a rule for differentiation. The answer key provided a simplified solution, but the person asking for help was stuck and needed further guidance.
  • #1
ishahad
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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 :(
 
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  • #2
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?
 
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  • #3
ishahad said:

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)
 
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  • #4
ishahad said:

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
[tex] f(x) = 6 - \frac{1}{x x} - 2 = 4 - \frac{1}{x^2}[/tex]
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
[tex]f(x) = 6 - \frac{1}{x(x-2)}[/tex]
then you need parentheses, like this: f(x) = 6 - 1/(x(x-2)). If you mean
[tex] f(x) = \frac{6 - (1/x)}{x} - 2[/tex]
then you need parentheses, like this: f(x) = (6 - (1/x))/x - 2. Finally, if you mean
[tex] f(x) = \frac{6 - (1/x)}{x-2}[/tex]
then use parentheses like this: f(x) = (6 - (1/x))/(x-2).
 
  • #5
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.
 
  • #6
Please, no more help, hints, or guidance until ishahad returns.
 

1. What is a derivation equation?

A derivation equation is a mathematical expression that describes the rate of change of a function with respect to its independent variable. It is used to find the slope of a curve at a specific point.

2. How do I solve a derivation equation?

Solving a derivation equation involves using mathematical techniques such as the power rule, product rule, and quotient rule. It also requires knowledge of basic algebra and trigonometry.

3. What is the purpose of solving a derivation equation?

The purpose of solving a derivation equation is to find the slope of a curve at a specific point, which is useful in many fields such as physics, engineering, economics, and more. It can also help in finding maximum and minimum values of a function.

4. Can I use a calculator to solve a derivation equation?

While a calculator can help with basic calculations, it is not recommended to solely rely on it for solving a derivation equation. It is important to understand the concepts and techniques used in solving these equations.

5. What are some tips for solving a derivation equation?

Some tips for solving a derivation equation include: understanding the basic rules and techniques, practicing regularly, and breaking down the equation into smaller, manageable steps. It is also helpful to familiarize yourself with common derivatives of functions.

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