Fraction Differentiation

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

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HallsofIvy
Homework Helper
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 :)

Mark44
Mentor

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

Mark44
Mentor
Since this is a calculus problem, I am moving it to the Calculus section.

Thank You

I have an exam tomorrow :(

Mark44
Mentor
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.

write this as (a + b)/2.
Thank you so much
but can you show me how can I write like this form above
TQ

Mark44
Mentor
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/.