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**Optimization problem -- Trouble differentiating function**

## Homework Statement

The efficiency of a screw, E, is given by

E=[tex]\frac{(\Theta - \mu\Theta^{2})}{\mu + \Theta} , \Theta > 0[/tex]

where [tex]\Theta[/tex] is the angle of pitch of the thread and [tex]\mu[/tex] is the coefficient of friction of the material, a (positive) constant. What value of [tex]\Theta[/tex] maximizes E?

## Homework Equations

[tex]\frac{f'g-g'f}{g^{2}}[/tex]

## The Attempt at a Solution

I know what to do once I have the derivative of the function, but for this particular function I've had trouble using the quotient rule (I didn't know how to turn it into the product rule, that would have been nice too). I came up with two possibilities and any help would be appreciated:

[tex]\frac{dE}{d\Theta}[/tex] = [tex]\frac{\mu - \mu^{2}2\Theta - \mu2\Theta^{2} - \Theta + \mu\Theta^{2}}{(\mu + \Theta)^{2}}[/tex]

and I also came up with

[tex]\frac{dE}{d\Theta}= \frac{-\mu2\Theta - 2\Theta^{2}}{(\mu + \Theta)^{2}}[/tex]

any help on which could be correct (or both wrong) would be greatly appreciated. I've read these forums a lot before and finally have a question of my own. Thanks for reading/help.