What am I doing wrong in finding the derivative and max/min?

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Homework Statement



I need to find the max/min of y=(1)/(3+x^2)

Homework Equations



y=(1)/(3+x^2)

The Attempt at a Solution



I tried to find the derivative; y'= (3+x)^-2(1) = -2(3+x)^-3 = -2/(3+x)^3 or -2/3(3+x)^2?

Whats wrong with it?
 
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Well, for starters, the derivative you calculated is wrong. What derivative rule are you using? Your attempt suggests some confusion.
 
Start off by using the chain rule (or quotient rule, whichever you prefer) to find the derivative of the function.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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