How to Correctly Apply the Quotient Rule in Differentiation?

DollarBill
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Homework Statement


X / 1+sinX

The Attempt at a Solution


Quotient rule

(1+sinX)(1)-X(1+cosX) / (1+sinX)2

To:

1+sinX-X-XcosX / (1+sinX)2

But when I look at the answer in the back of the book, it's wrong.
 
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Is the derivative of 1+sinX really 1+CosX? I thought the derivative of 1 was zero. ;0)
 


I always make these stupid mistakes

Thanks :biggrin:
 

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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