Why is the second derivative expressed differently in Lebnit's notation?

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In summary, the conversation discusses the notation for the second derivative in calculus and clarifies that it is not expressed as d²y/d²x², but rather as d²y/dx². The conversation also includes an analogy to explain the meaning of dx in this context.
  • #1
Juxt
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I am in my first year of calculus at the high school level so be patient with me.

Why is it that in Lebnit's (spelling?) notation the second derivative is expressed as d²y/dx² ? My instructor did not know and from what we could work out it seems as if it should be expressed as d²y/d²x².

We have covered about what you have covered in the first eighth of a college level calculus course so try not to go too far over my head.:smile:
 
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  • #2
Hi Juxt, and welcome to PF.

The second derivative is just the first derivative of the first derivative. :smile:

Mathematically, the above sentence translates to:

d2y/dx2=(d/dx)(d/dx)y

You can loosely think of the two operators on the right as being multiplied like fractions to get:

(d2/dx2)y

or simply:

d2y/dx2.

edit: fixed typo
 
  • #3
Maybe I was confused... is does dx= d times x or is dx like one variable (dx)? I am assuming that dx= d times x, as such I don't understand why it isn't d²y/d²x². Is my perception of the nomenclature wrong?
 
  • #4
Originally posted by Juxt
Maybe I was confused... is does dx= d times x or is dx like one variable (dx)?

The second one.

dx is what you get when you take Δx(=x2-x1) and pass to the limit Δx-->0. Just as Δx is not Δ times x, so dx is not d times x.
 
  • #5
Thank you for that terrific analogy. What a lightbulb.
 
  • #6
lol taking calculus in high school rofl.
 

1. What is Lebnit's notation?

Lebnit's notation is a mathematical notation system developed by the German mathematician and philosopher Gottfried Wilhelm Leibniz. It is used to represent derivatives and integrals, and is a fundamental tool in calculus and other branches of mathematics.

2. How is Lebnit's notation different from other mathematical notations?

Unlike other notations, Lebnit's notation uses a combination of letters and symbols to represent derivatives and integrals. For example, the derivative of a function f is represented as df/dx, and the integral of a function f is represented as ∫ f(x) dx.

3. When is Lebnit's notation used?

Lebnit's notation is used primarily in calculus and other branches of mathematics, as it provides a concise and elegant way to represent derivatives and integrals. It is also commonly used in physics and engineering.

4. What are the advantages of using Lebnit's notation?

One of the main advantages of Lebnit's notation is its flexibility and ease of use. It allows for a more intuitive understanding of derivatives and integrals, as well as making complex mathematical equations easier to write and understand. It also allows for a more compact representation of mathematical concepts.

5. Are there any drawbacks to using Lebnit's notation?

While Lebnit's notation is widely used and accepted, some may argue that it can be more difficult to interpret for those who are not familiar with it. Additionally, there may be some variations in the use of symbols and letters within the notation system, leading to potential confusion. However, these drawbacks are minor and do not diminish the usefulness of Lebnit's notation.

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