Fraction Differentiation

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).

 

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

 

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.

 

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/.