Does a Function f(x,y,z) Satisfy Given Partial Derivatives?

In summary, "Proof that function exists" is a mathematical concept that states every input has a corresponding output. Its existence can be proven through mathematical techniques like induction, contradiction, or direct proof. Proving the existence of a function is important for its validity and usability in calculations and applications. While a function can technically exist without proof, it cannot be considered a valid mathematical concept. Real-world examples of this concept include the relationship between distance, time, and speed, which can be represented by the function d=rt.
  • #1
kokai
1
0
[itex]f(x,y,z)[/itex] is function that:
[itex]
x^{q-1}\frac{\partial f}{\partial x}=
y^{q-1}\frac{\partial f}{\partial y}=
z^{q-1}\frac{\partial f}{\partial z}
[/itex].

How to prove that exists function [itex]g[/itex]:
[itex]f(x,y,z)=g(x^q+y^q+z^q)[/itex]
 
Physics news on Phys.org
  • #2
Have you tried doing the differentiation?
 

FAQ: Does a Function f(x,y,z) Satisfy Given Partial Derivatives?

What is "Proof that function exists"?

"Proof that function exists" is a mathematical concept that states that for every input, there is a corresponding output. In simpler terms, it means that every action or operation has a predictable result.

How is the existence of a function proven?

The existence of a function can be proven through mathematical techniques such as mathematical induction, contradiction, or direct proof. These methods use logical reasoning and mathematical principles to show that a function exists and is valid.

Why is it important to prove the existence of a function?

Proving the existence of a function is crucial in mathematics because it provides a solid foundation for further analysis and calculations. It ensures that the function is well-defined and can be used for various applications and problem-solving.

Can a function exist without being proven?

Technically, yes, a function can exist without being proven. However, without proof, it cannot be considered a valid mathematical concept and cannot be used in mathematical calculations and applications.

Are there any real-world examples of "Proof that function exists"?

Yes, there are many real-world examples of "Proof that function exists." For instance, the relationship between distance, time, and speed can be represented by the function d=rt, where d is the distance traveled, r is the speed, and t is the time taken. This function has been proven to exist and can be used in various situations, such as calculating travel time or fuel consumption.

Similar threads

I Partial derivatives of the function f(x,y)
Replies
6
Views
2K
I How to manipulate functions that are not explicitly given?
Replies
16
Views
1K
I An attempt to find the total differential of a two-variable function
Replies
6
Views
1K
I Lipschitz continuity of vector-valued function
Replies
3
Views
2K
MHB Evaluate the surface integral $\iint\limits_{\sum}f\cdot d\sigma$
Replies
1
Views
2K
I Determination of error in interpolating polynomial
Replies
5
Views
1K
I From a proof on directional derivatives
Replies
9
Views
2K
I The Euler-Lagrange equation and the Beltrami identity
Replies
1
Views
2K
A Partial / Total Derivative, Compositions
Replies
4
Views
2K
A Dirac delta function confusion
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top