# Fraction Differentiation

• red1312
In summary, the equation you are trying todifferentiate has an error in the numerator, and the result is incorrect.
red1312

## Homework Statement

Differentiate the following functions with respect to x

(√2x-1)/ (lnx)?

## The Attempt at a Solution

ln x (2x-10)^-1/2 -√(2x-1)(1/x)/(ln x)^2
..........{This is a denominator}
thank you

[/B]

The only error I see is an obvious typo- that "2x- 10" should be "2x- 1".

So it is right ?

there is no any factor right ?!
and this is the last answer isn't it ?

Thank you :)

red1312 said:

## Homework Statement

Differentiate the following functions with respect to x

(√2x-1)/ (lnx)?

## The Attempt at a Solution

ln x (2x-10)^-1/2 -√(2x-1)(1/x)/(ln x)^2
..........{This is a denominator}
thank you
[/B]
The function (it's not an equation) you are differentiating is ambiguous. You wrote √2x-1 as the numerator. Which one of these did you mean?
1. ##\sqrt{2}x - 1##
2. ##\sqrt{2x} - 1##
3. ##\sqrt{2x - 1}##
From your answer, it seems that what you intended was #3 above. If you use the √ for square roots, use parentheses to indicate what's inside the radical, like so: √(2x - 1).

Sorry for that

I was meaning the third one :)

TQ

Since this is a calculus problem, I am moving it to the Calculus section.

Thank You

I have an exam tomorrow :(

red1312 said:
ln x (2x-10)^-1/2 -√(2x-1)(1/x)/(ln x)^2
As already mentioned, 2x - 10 should be 2x - 1.

Also, as you wrote the above, it would be incorrect. You need parentheses or brackets around the entire numerator -- [ln x (2x-1)^(-1/2) -√(2x-1)(1/x)]/(ln x)^2 -- and you should have parentheses around the -1/2 exponent.

Regarding the numerator, if you write a + b/2, this is seen by almost everyone as a + (b/2). To make your intentions clear, write this as (a + b)/2. That was my point in the previous paragraph.

Mark44 said:
write this as (a + b)/2.

Thank you so much
but can you show me how can I write like this form above
TQ

red1312 said:
Thank you so much
but can you show me how can I write like this form above
TQ
Do you mean using LaTeX?
If so, here's what I wrote in post #4,
1. # #\sqrt{2}x - 1# #
2. # #\sqrt{2x} - 1# #
3. # #\sqrt{2x - 1}# #
Each pair of # # characters should be written WITHOUT the extra space. With the extra space, you can see the LaTeX script without it being rendered in the browser.

The # # pairs are used for inline LaTeX. For standalone LaTeX, use  (again, without the spaces). You can also use [ itex] and [ /itex], or [ tex] and [ /tex] tags at the beginning and end of your expressions. I prefer to use # # pairs or sometimes  pairs, since they require less typing.
For a brief tutorial on LaTeX, see https://www.physicsforums.com/help/latexhelp/.

## 1. What is fraction differentiation?

Fraction differentiation is a mathematical method used to find the rate of change of a function with respect to a fraction variable. It can be thought of as a generalization of the derivative, which finds the rate of change with respect to a whole number variable.

## 2. How is fraction differentiation different from regular differentiation?

Fraction differentiation involves finding the derivative with respect to a fraction variable, while regular differentiation only considers whole number variables. Additionally, the rules and formulas for fraction differentiation are slightly different than those for regular differentiation.

## 3. What are the applications of fraction differentiation?

Fraction differentiation has many applications in fields such as physics, economics, and engineering. It can be used to find the optimal solution for problems involving fractions, as well as in the analysis of complex systems.

## 4. Can fraction differentiation be used for both simple and complex functions?

Yes, fraction differentiation can be used for both simple and complex functions. The rules and formulas for fraction differentiation apply to any function that involves a fraction variable, regardless of its complexity.

## 5. Are there any limitations to fraction differentiation?

One limitation of fraction differentiation is that it can only be applied to functions that involve a fraction variable. It cannot be used for functions that do not contain a fraction, or for functions that cannot be expressed as a fraction. Additionally, some functions may require more advanced techniques to find their derivatives.

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