Solving for Partials: ∂u/∂x Explained

  • Thread starter Zeth
  • Start date
In summary, the conversation is about solving for the partial derivative of u with respect to x using implicit differentiation, with the specific equations given being x = u + v + w, y = u^2 + v^2 + w^2, z = u^3 + v^3 + w^3. The answer is ∂u/∂x = (vw)/((v − u)(w − u)). The person is unsure about the method and asks for clarification.
  • #1
Zeth
23
0
"Solving for Partials"

This is for my revision and I have the answer sheet:

I'm meant to find ∂u/∂x for x = u + v + w, y = u^2 + v^2 + w^2, z = u^3 + v^3 + w^3

That as far as I can tell, by a miracle, is meant to equal:

∂u/∂x=(vw)/((v − u)(w − u))

All the question says apart from find this is "Solving for Partials".

I can't find anything that looks like this in my notes and google comes up empty. What's going on here?
 
Physics news on Phys.org
  • #2
Well, if you want to solve for the partial derivative of u with respect to x, it seems that you ought to partially differentiate each equation with respect to x. What kind of equations do you get when you do that?
 
Last edited:
  • #3
key word : implicit differentiation
 

FAQ: Solving for Partials: ∂u/∂x Explained

What is the purpose of solving for partials (∂u/∂x)?

Solving for partials is important in mathematics and science because it allows us to understand the relationship between two variables in a multivariable function. It helps us to analyze how a change in one variable affects the value of another variable.

How do you solve for partials (∂u/∂x)?

To solve for partials, you must hold all other variables constant and differentiate the function with respect to the variable in question. This means treating all other variables as constants and taking the derivative with respect to the variable in question.

Why is it important to understand partial derivatives?

Partial derivatives are important in many fields of science and engineering, such as physics, economics, and engineering. They allow us to model complex systems and understand how changes in one variable impact other variables. This is crucial for making predictions and optimizing systems.

What are some real-world applications of solving for partials (∂u/∂x)?

Partial derivatives are used in many real-world applications, such as optimizing production processes in manufacturing, modeling changes in stock prices in finance, and understanding fluid flow in engineering. They are also used in physics to understand the relationship between different physical quantities in complex systems.

Are there any limitations to solving for partials (∂u/∂x)?

While solving for partials is a powerful tool, it does have some limitations. It assumes that all other variables are held constant, which may not always be the case in real-world scenarios. Additionally, it may not be possible to solve for partials in some functions, particularly in non-linear systems.

Similar threads

Multivariable calculus proof involving the partial derivatives of an expression
Replies
4
Views
987
Finding a complementary subspace ##U## | Linear Algebra
Replies
4
Views
2K
Solving this partial differential equation
Replies
7
Views
2K
Solving this integral with u substitution
Replies
11
Views
2K
MacKay Textbook Example: Laplace Approximation
Replies
1
Views
1K
Given subspaces ##U \& W##, show they are equal | Linear Algebra
Replies
8
Views
1K
"Trick" for a specific potential function defined with an integral
Replies
10
Views
2K
Solve the given first order PDE
Replies
5
Views
1K
Finding the dimension of a subspace
Replies
7
Views
2K
Exploring the Structure of the Poisson Equation
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top