dx of ln(x) where is a rational function

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I don't understand what is going on in the second to last line of this. I'm doing something wrong when I get there.

I think it's really just an algebra mistake but I can't seem to see it.

What is it that you get? Without seeing your work, I can't say where you are going wrong.

There's a lot of chain rules to bear in mind. Just try to keep track of them all, making sure that you cancel and simplify at each stage. It should make sense after that.

If not, just write the first stage down and try to do it all yourself.

In doing what particularly are you struggling?

Michael