Not Understanding Derivative Notation

In summary, the speaker is having trouble understanding a step in an example problem from their Classical Mechanics book. They specifically mention not understanding how the left hand side goes from the first step to the second step. They also mention having a poor understanding of Leibniz notation. Another speaker then explains that it is just using the product rule in reverse. The original speaker thanks them and admits they should have probably posted in a different section.
  • #1
Gibby_Canes
21
0
In my Classical Mechanics book, one of the example problems makes a step that I do not understand. The steps are in the picture in the attachment. I do not understand how the left hand side goes from what it is in the first step to what it is in the second step. I have a poor understanding of Leibniz notation, so please keep that in mind in your responses.
 

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  • #2
This is just taking the product rule in reverse.

[tex]2 \dot x \ddot x = 2 v v' = (v v' + v' v) = (v^2)'[/tex]
 
  • #3
Wow thanks. I do not know why that had me so stumped. I should probably sleep more.

Also, I just realized this probably should've been posted elsewhere. I was doing mechanics so I just went straight to the mechanics section. Apologies to anyone reading this.
 

1. What is derivative notation?

Derivative notation refers to the mathematical notation used to represent the derivative of a function. It typically involves the use of symbols such as f'(x) or dy/dx to represent the rate of change of a function at a specific point.

2. Why is derivative notation important?

Derivative notation is important because it allows us to express the rate of change of a function in a concise and precise manner. It is also a fundamental concept in calculus, which is a branch of mathematics that is widely used in various fields of science and engineering.

3. How do I read derivative notation?

Derivative notation can be read as "the derivative of the function f with respect to x" or "the rate of change of f with respect to x". The notation f'(x) can also be read as "the derivative of f at x" or "the value of the derivative of f at x".

4. What is the difference between f'(x) and f(x)?

The notation f'(x) represents the derivative of a function f, while f(x) represents the function itself. In other words, f'(x) represents the rate of change of f at a specific point, while f(x) represents the value of f at that point.

5. How can I improve my understanding of derivative notation?

To improve your understanding of derivative notation, it is important to first have a solid understanding of basic calculus concepts such as limits, continuity, and differentiation. Additionally, practicing with various examples and problems can also help improve your understanding and familiarity with derivative notation.

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