Simplify derivative after using product and chain rule

biochem850
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Homework Statement



(x^{2}-x^{-1}+1)(x^{3}+2x-6)^{7}

Homework Equations


Chain Rule & Power Rule

The Attempt at a Solution



(x^{3}+2x-6)^{6}[(x^{3}+2x-6)(2x+x^{-2})+7(3x^{2}+2)(x^{2}-x^{-1}+1)]

This is the farthest I've gotten but when I do additional computation I do not arrive at the correct simplified solution.

edit- should be "simplify derivative after using power rule and chain rule"

Homework Statement

Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
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hi biochem850! :wink:

looks ok so far :smile:

you've probably made a mistake with a minus somewhere later …

check them first …

if that doesn't help, then show us what you did​
 
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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