Question about the use of Leibniz notations …

  • Thread starter Pellefant
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    Leibniz
In summary, the article states that u(x)*dy/dx=d(y*u)/dx. This is the product rule. If you want to write u(x)*y(x)d/dx, you need to apply the d/dx operator to y first.
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  • #2
Please don't take offense, and by the way welcome to Physics forums, but i very strongly recommend that you borrow a nice calculus book from the library, or purchase one if you are able to, because I can see from your other post that you have no previous experience with the topic. The parts of calculus your posts are on are quite far apart in level of difficulty, and you should really start with the basics. mathwonk recommends "calculus made easy" often for beginners, though I can't recall the author, try googling it.
 
  • #3
I have math books, but this i could just not understand this ...
:(, well i know that i suck at math ..

Anyway:
If i have understand it correct, can i write "u(x)*dy/dx" as:
"u(x)*y(x)d/dx"

Kindly Pellefant ... if that is so then i will be pleased ...

Anyway i think you may ahve a point in what you said ...
 
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  • #4
Also i have read math in university level but it was awhile ago now, and then i just studied before the exame. Now i won't to put my math knowledge back on track, but you must laugh at me and thinking i am a idiot ...
 
  • #5
  • #6
And "u(x)*y(x)d/dx" makes no more sense than "u sin(y)= uy sin"!

"d/dx" is an operator- it has to be applied to something- and that something, by standard notation is written on the right.
 
  • #7
HallsofIvy said:
And "u(x)*y(x)d/dx" makes no more sense than "u sin(y)= uy sin"!

"d/dx" is an operator- it has to be applied to something- and that something, by standard notation is written on the right.

I see the reason i got that idea was because my math book wrote dy/dx as (d/dx)*y ...

So my math book stated dy/dx = (d/dx)*y
 
  • #8
Double check what the textbook actually wrote if it wrote (d/dx)*y to mean dy/dx then throw it away.

More likely you have misinterpreted the text. Is it possible to scan the page and include it in your next post?
 
  • #9
kk but u can write it as:

du/dx= d/dx (x^-1) where u = (x^-1)

And anouther question, i wonder purely academically, would it be ok to do the following

y=x^2+4x+5

dy/dx=d(x^2+4x+5)/dx

........

Oki i think i get much of it but (if you find me annoying just ignore to reply :))

I don't get how he can make this assumption
u(x) dy / dx + u(x) P(x) y = y du / dx + u dy / dx
which would mean
du / dx = u(x) P(x)

My question is if this proof from the first link in the topic is complete? ...
 
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  • #10
I wonder if many of those proof r correct purely mathematicaly ... here is anouther one ...

http://www.bio.brandeis.edu/classes/biochem102/hndDiffEq.pdf [Broken]

look at (3) before they can put out the constant of integration, they has to do the integration, right?
 
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  • #11
Pellefant said:
I see the reason i got that idea was because my math book wrote dy/dx as (d/dx)*y ...

So my math book stated dy/dx = (d/dx)*y
1: I'll bet the book does NOT have that "*" which implies multiplication. What (d/dx)y means is "the differentiation operator applied to the function y".

2: And did you notice that the y is to the right of the d/dx ?

It may be you are confusing (d/dx)y with multiplication which is commutative. Applying an operator is not- as in my example above "sin x" is NOT the same as "x sin"!
 
  • #12
Sorry, my fault

~ Pellefant ...

/and thank you for your reply, this has been learning for me ...
 
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1. What is the significance of Leibniz notations in mathematics?

Leibniz notations, also known as differential notations, are a widely used mathematical notation for expressing derivatives and integrals. They were introduced by German mathematician and philosopher Gottfried Wilhelm Leibniz in the 17th century and have become an integral part of calculus and other branches of mathematics.

2. How are Leibniz notations different from other mathematical notations?

Leibniz notations use a unique symbol, d, to represent the derivative of a function, while other notations may use f' or y'. Additionally, Leibniz notations use a fraction-like format, with the derivative on top and the variable of differentiation at the bottom, making them easier to read and understand.

3. Can Leibniz notations be used for higher-order derivatives?

Yes, Leibniz notations can be extended to represent higher-order derivatives, such as the second derivative (d2y/dx2) and third derivative (d3y/dx3). This makes it a versatile notation for expressing complex mathematical concepts.

4. Are there any limitations to using Leibniz notations?

While Leibniz notations are widely used and accepted, they are not without limitations. Some mathematical concepts, such as partial derivatives and vector calculus, may require the use of other notations. Additionally, some may argue that Leibniz notations are not as precise as other notations, as they do not explicitly show the limit in the definition of a derivative.

5. How can I learn more about Leibniz notations?

There are many online resources and textbooks available that explain Leibniz notations in detail. It is also helpful to practice using them in various mathematical problems to become more familiar with their applications. Additionally, studying the history and development of calculus can provide a deeper understanding of the significance of Leibniz notations.

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