Derivative of ln3: Simple Problem Solution

  • Thread starter BuBbLeS01
  • Start date
  • Tags
    Derivative
In summary, the derivative of ln(2x^2 + 3) is (4x)/(2x^2 + 3) or (2x)/(x^2 + 3). This is found by using the property of logs, ln(ab) = ln(a) + ln(b), and differentiating ln(x^2 + 3) to get (2x)/(x^2 + 3).
  • #1
BuBbLeS01
602
0

Homework Statement


ln (2x^2 + 3)


Homework Equations


ln 2x^2 + ln 3


The Attempt at a Solution


(4x/2x^2) + (3/3)
(2x/x^2) + 1

I know this is a simple problem but what is the derivative of ln3? Is it 1 (3/3) or 0?
 
Physics news on Phys.org
  • #2
properties of logs

[tex]\ln(ab)=\ln(a)+\ln(b)[/tex]

what you have is

[tex]\ln(a+b)=\ln(a+b)[/tex]

example

[tex]\ln(x^{2}+3)[/tex]

differentiating

[tex]\frac{2x}{x^{2}+3}[/tex]
 
Last edited:
  • #3
rocophysics said:
example

[tex]\ln(x^2)[/tex]

differentiating

[tex]\frac{2x}{x^2}[/tex]

properties of logs

[tex]\ln(ab)=\ln(a)+\ln(b)[/tex]
Can't you distribute the ln to get lna + lnb? I don't know what the derivative of ln3 is? Is it 3/3 or 0/3.
 
  • #4
BuBbLeS01 said:
Can't you distribute the ln to get lna + lnb? I don't know what the derivative of ln3 is? Is it 3/3 or 0/3.
i just updated my post, i clicked submit on accident while trying to preview.
 
  • #5
Oh okay I see now. So it would be...
(4x)/(2x^2 + 3)
(2x)/(x^2 + 3)
 

FAQ: Derivative of ln3: Simple Problem Solution

What is a simple derivative problem?

A simple derivative problem is a mathematical question that involves finding the rate of change of a function at a specific point. It is a fundamental concept in calculus and is used to solve real-world problems involving rates of change.

How do you solve a simple derivative problem?

To solve a simple derivative problem, you need to use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules help you find the derivative of a function, which represents the rate of change of the function at a specific point.

What are the common applications of simple derivative problems?

Simple derivative problems have many applications in fields such as physics, engineering, economics, and biology. They are used to calculate rates of change in various processes, such as velocity, acceleration, growth, and decay.

Can you provide an example of a simple derivative problem?

Sure, an example of a simple derivative problem would be finding the derivative of the function f(x) = 3x^2 at x = 2. Using the power rule, we get f'(x) = 6x. Substituting x = 2, we get f'(2) = 6(2) = 12. Therefore, the rate of change of the function at x = 2 is 12.

What are some tips for solving simple derivative problems?

Some tips for solving simple derivative problems include practicing the differentiation rules, understanding the concepts of rate of change and slope, and breaking down the problem into smaller steps. It is also helpful to check your answers using a graphing calculator or online tool.

Similar threads

Replies
6
Views
579
Replies
4
Views
379
Replies
7
Views
1K
Replies
47
Views
2K
Replies
25
Views
1K
Replies
1
Views
650
Replies
4
Views
1K
Replies
9
Views
2K
Replies
1
Views
1K
Back
Top