Derivative of Natural Log: How to Solve Number 3 on Homework Assignment

thegoosegirl42
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Homework Statement


I posted a picture of it and my attempt it is number 3

Homework Equations

The Attempt at a Solution


I tried using log properties and I am not sure what went wrong and how to arrive at the correct answer.

Mod note: Messy, disorganized image deleted.
 
Last edited by a moderator:
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log derivative and chain rule should get you there.
 
You need to brush up on your algebra. ##\sqrt[3]{x}## doesn't mean ##(\sqrt{x})^3##; it means ##x^{1/3}##. Try again.
 
If you must post your attempt at a solution in handwritten form, at least use a clean sheet of paper and present your work in some logical sequence so that others can follow it. o_O
 
@thegoosegirl42,
The image you posted was so bad that I deleted it. Please post the problem you want help on (not an image), together with your work.
 

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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