Math Differentiation Review: Simplifying with Basic Equations

tandoorichicken
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For higher math classes, its trivial to say that if y=x, then y'=1. Higher level textbooks also don't review a lot of the basics that are easy to forget.

So if you have an equation that looks like y=x(t), then even if dy/dt might be some complicated looking function in t, dy/dx is still just =1 right?
 
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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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