- #1

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## Homework Statement

I'm try to implicitly differentiate the function: xlny+√y=lnx

## The Attempt at a Solution

And I got to the stage where I have: dy/dx = (1/x-lny)/(x/y+1/(2*√y)) which is where I have no idea on how to clean this up. Could someone please explain to me how to simplify a function like that?

Im not quite sure if I was heading to the right anwer but anyway the book provided the answer of

(2y-2xylny)/(2x^2+x√y).

Either way I would like to know how to simplify an equation like the one I have as I've come across it a few times.

Thanks for your help in advance.