Discovering the Derivate Definition for f(x) = x/(2x-1): A Step-by-Step Guide

  • Thread starter ladyrae
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In summary, the conversation discusses finding the derivative of f(x) = x/(2x-1) using the definition of derivative. The derivative is calculated as lim h->0 [(f(x+h)) – (f(x))]/h which simplifies to -1/(2x-1)^2. The speaker also suggests using LATEX formatting and continuing to use the same thread for further questions.
  • #1
ladyrae
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0
Thanks for your help...

How about this one?

Using the definition of derivate find f ` (x)

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

f ` (x) = lim h->0 [(f(x+h)) – (f(x))]/h

lim h->0 ([((x+h) / (2x+2h-1))-(x/(2x-1))]/h) . [((2x+2h-1)(2x-1)) / ((2x+2h-1)(2x-1))]

lim h->0 [(2x^2)-x+(2xh)-h-(2x^2)-(2hx)+x]/(h(2x+2h-1)(2x-1))

lim h->0 -h/(h(2x+2h-1)(2x-1)) = -1/(2x-1)^2
 
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  • #2
If f(x)=x/(2x-1), then it is correct.
 
  • #3
typo

yes...thanks
 
  • #4
just a suggestion, ladyrae:
if you have more questions on this, don't open any new thread, continue to use this instead.
In addition, try to learn LATEX formatting, it's not very difficult..
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It can be thought of as the slope of a curve at a particular point. In other words, it tells us how much a function is changing at a specific point.

Why is it important to find the derivative?

Finding the derivative of a function allows us to understand the behavior of the function, such as whether it is increasing or decreasing at a specific point. It also helps us to find the maximum and minimum values of a function, which are useful in many real-world applications.

How do you find the derivative of a function?

The derivative of a function can be found using the derivative definition, which is the limit of the difference quotient as the change in the input approaches zero. This is also known as the first principle of differentiation. It involves finding the slope of the tangent line at a specific point on the function.

What is the derivative definition for f(x) = x/(2x-1)?

The derivative definition for f(x) = x/(2x-1) is the limit of the difference quotient (f(x+h) - f(x))/h as h approaches zero. This can be simplified to 1/(2x-1)^2, which represents the slope of the tangent line at any point on the function.

Why is it important to show the step-by-step process of finding the derivative?

Showing the step-by-step process of finding the derivative allows others to understand the concept and apply it to other functions. It also helps to avoid errors and provides a clear explanation of the solution. Additionally, it helps to develop problem-solving skills and critical thinking abilities.

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