# Help me solving a Derivation equation

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.

## Homework Statement

find the derivative of the given function:

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

## 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 :(

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?

1 person

## Homework Statement

find the derivative of the given function:

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

## 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)

Last edited:
1 person

## Homework Statement

find the derivative of the given function:

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

## 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).

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.

## 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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