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

In summary, the conversation was about a homework problem involving logarithmic properties and the chain rule. The person attempted to solve it by using the wrong algebraic operation for a cube root, but was advised to try again using the correct operation. They were also reminded to present their work in a clear and organized manner for others to follow.
  • #1
thegoosegirl42
22
1

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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  • #2
log derivative and chain rule should get you there.
 
  • #3
You need to brush up on your algebra. ##\sqrt[3]{x}## doesn't mean ##(\sqrt{x})^3##; it means ##x^{1/3}##. Try again.
 
  • #4
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
 
  • #5
@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.
 

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

What is the derivative of ln(x)?

The derivative of ln(x) is 1/x.

Why is the derivative of ln(x) equal to 1/x?

The derivative of ln(x) is equal to 1/x because ln(x) is the inverse of the natural logarithmic function e^x. Thus, the derivative of ln(x) is the inverse of the derivative of e^x, which is 1/x.

What is the general rule for finding the derivative of a natural log?

The general rule for finding the derivative of a natural log function, ln(x), is to take the inverse of the function inside the ln and multiply it by the derivative of the function inside the ln.

How do you find the derivative of ln(u), where u is a function of x?

To find the derivative of ln(u), where u is a function of x, you must use the chain rule. Take the derivative of ln(u) as if u was a variable, and then multiply it by the derivative of u with respect to x.

What is the derivative of ln(f(x))?

The derivative of ln(f(x)) is 1/f(x) * f'(x), or simply f'(x)/f(x). This can also be written as (f(x))'/f(x), where (f(x))' is the derivative of f(x).

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