Why Does My Answer Differ from the Textbook in Differentiating y = x(1+x)^0.5?

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Hey guys I am having a bit of trouble solving the following problem,
differentiate y = x ((1+x)^0.5)
I am using the product rule however I am getting a different answer to the back of my textbook I was wondering if anyone could help clear this up for me, thanks.
 
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What are you getting and how are you getting it? What does the book say?
 

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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