How to Correctly Apply the Power Rule in Calculus?

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Homework Statement


y=(X^5/6) + (1/10X^3)


Homework Equations





The Attempt at a Solution


5X^4 - 30X^2
 
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can anyone please confirm it so I can proceed with the problem. thank you
 
Without tex it is hard to see what the original equation is. Either way, both terms look incorrect. Was this your original equation?

y = \frac{x^5}{6} + \frac{1}{10 x^3}

What does the power rule say for derivatives?
 

Thread 'Finding the nth roots of a complex number'

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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