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

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To solve the derivative of the natural log in question number 3, it's essential to apply the correct log properties and the chain rule. The original attempt was hindered by a misunderstanding of the notation for cube roots, which should be expressed as x raised to the power of one-third, not as the cube of the square root. A clearer presentation of the work is necessary for effective assistance, as messy or disorganized submissions can lead to confusion. It is advised to use clean paper and logical sequencing in future submissions. Proper algebra skills are crucial for arriving at the correct answer.
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.
 
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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.
 

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