Solving Derivative of f(x) = 1/2x^2 + 3x^3 - Is My Answer Correct?

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I'm having problem

finding derivative:
f(x) = 1/2x^2 + 3x^3

i know there is a shortcut way to derivative, but i did the long way and got

9x^2 - x

is that correct? if not, can you tell me the step to solve it? thanks
 
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If you're trying to find the derivative, you use the power rule by bringing down the power and then taking the power that the variable was raised to and subtracting one...I hope that makes sense...
 
ok thanks alot,
 
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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