Not understanding how the author rearranged this log into what he did?

Achooie

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Sep 8, 2017
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Hi all,

I finished the math I needed for my degree last year. I'm now taking an economics course and have run into a pickle. It's not the math I have trouble with, it's the way the author rearranged the expression! We were asked to take the derivative of the top function. Somehow this was to change into the part you see at the bottom. I understand taking the derivative of a log means c/x for the first one, but someone told me I was wrong about how I approached the second part. I just put d/(m/p2 - p1/p2*x1). I'm ashamed to admit I forgot a few of the finder details here. I've racked my brain for hours to figure this out to no avail. I would really appreciate the help!

I've tried using the chain rule but feel I'm doing something wrong; if u = m/p2 - p1/p2*x1, then y = ln u, and that means u'/u. It's at this point I'm stuck because I don't understand how to take the derivative of a function when all I have to work with is letters. Please assist, and thank you! :)



043a693ea5.png
 
It looks good. Hard to say where you are wandering off. Would it help to write it like this?

\(\displaystyle \dfrac{c}{x_{1}} + d\cdot\dfrac{1}{\left(\dfrac{m}{p_{2}}-\dfrac{x_{1}p_{1}}{p_{2}}\right)}\cdot\left(-\dfrac{p_{1}}{p_{2}}\right)\)

The rest is algebra.
 
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