What is the Meaning of dy/dx in Nonstandard Calculus?

  • Context: Graduate 
  • Thread starter Thread starter vkash
  • Start date Start date
Click For Summary
SUMMARY

The discussion clarifies that dy/dx is the Leibniz notation for the derivative, representing the derivative of y with respect to x, rather than a simple division of dy by dx. It emphasizes that in the context of the equation y=x², the derivative is found using implicit differentiation, resulting in the expression 1*dy/dx=2x. Additionally, it notes that in nonstandard calculus, dy/dx can be interpreted as dy divided by dx when using infinitesimals instead of limits.

PREREQUISITES
  • Understanding of derivatives and Leibniz notation
  • Familiarity with implicit differentiation
  • Basic knowledge of nonstandard calculus concepts
  • Proficiency in algebraic manipulation of equations
NEXT STEPS
  • Study the principles of implicit differentiation in calculus
  • Explore the differences between standard and nonstandard calculus
  • Learn about the use of infinitesimals in calculus
  • Review the historical context and applications of Leibniz notation
USEFUL FOR

Students of calculus, mathematics educators, and anyone interested in advanced calculus concepts, particularly those exploring the nuances of derivatives and nonstandard approaches to calculus.

vkash
Messages
316
Reaction score
1
...
 
Physics news on Phys.org
micromass said:
It's the Leibniz notation for the derivative. See http://en.wikipedia.org/wiki/Derivative
very long article.
Actually the thing i want to ask is Does dy/dx means dy divided by dx.
 
vkash said:
very long article.
Actually the thing i want to ask is Does dy/dx means dy divided by dx.


Not at all! dy/dx is simply a notation. It's a notation for the derivative with respect to y.
 
It means the same thing as f'(x) does. Take whatever y is and take the derivative of it with respect to x.
If we have the equation, {y=x^2} what's the derivative with respect to x? We have to use implicit differentiation because you can't the derivative of y when we are taking it it with respect to x. So you have {1*dy/dx=2x}

Hopefully my explanation is clear haha.
 
It does, in some sense, mean \mathrm dy divided by \mathrm dx in nonstandard calculus, where we use infinitesimals instead of limits to do calculus.
 

Similar threads

High School What Is the Meaning of $\frac{d}{dx} \frac{dy}{dx}$?
  • · Replies 10 ·
Replies
10
Views
2K
MHB Question about the differential in Calculus
  • · Replies 9 ·
Replies
9
Views
2K
High School Why is Delta y not equal to dy for infinitesimally dx on the graph?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad What is the meaning of dx and how does it relate to dy/dx?
  • · Replies 11 ·
Replies
11
Views
6K
Undergrad What are differentials and how are they used in calculus and physics?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad The Euler-Lagrange equation and the Beltrami identity
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Why Does dV Equal ∂V/∂x(dx) + ∂V/∂y(dy)?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Integration of ##e^{-x^2}## with respect to ##x##
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What is dx, dy and dz in spherical coordinates
  • · Replies 7 ·
Replies
7
Views
10K
High School Is dy/dx of x2+y2 = 50 the same as dy/dx of y = sqrt(50 - x2)?
  • · Replies 3 ·
Replies
3
Views
2K