Expressed all partial derivatives

Then, using the result, express (∂z/∂x)*x+(∂z/∂y)*y in terms of u and v.In summary, the conversation is about trying to prove that (∂z/∂x)*x+(∂z/∂y)*y=3*z using the given function F(x*y;z/x) and expressing the partial derivatives in terms of u and v. The speaker is struggling with finding the correct solution and is seeking help.
  • #1
Yegor
147
1
I'm given F(x*y;z/x), where z=z(x,y).
I have to proof that (∂z/∂x)*x+(∂z/∂y)*y=3*z
I have expressed all partial derivatives, but I got only (∂z/∂x)*x-(∂z/∂y)*y=z
I think that it's impossible at all to solve this problem, because z is arbitrary function as i understand.
Help me please. Where I'm wrong?
 
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  • #2
I made it. And received (∂z/∂x)*x-(∂z/∂y)*y=z
Did anyone get (∂z/∂x)*x+(∂z/∂y)*y=3*z ??
I've denoted already many hours for this problem and many times got "incorrect" answer. Now I think that my solution is correct and something is wrong with a "handwritten answers" on the sheet with problems
 
  • #3
Yegor said:
I'm given F(x*y;z/x), where z=z(x,y).
I have to proof that (∂z/∂x)*x+(∂z/∂y)*y=3*z
I have expressed all partial derivatives, but I got only (∂z/∂x)*x-(∂z/∂y)*y=z
I think that it's impossible at all to solve this problem, because z is arbitrary function as i understand.
Help me please. Where I'm wrong?

Have you stated the problem correctly?

Consider the variables u = x*y and v = z/x and take the partial derivatives of F using the chain rule
 

1. What is the concept of "expressed all partial derivatives"?

"Expressed all partial derivatives" is a mathematical concept that refers to the process of taking the partial derivatives of a multi-variable function with respect to each of its independent variables and organizing them into a matrix or vector.

2. Why is it important to understand "expressed all partial derivatives"?

Understanding "expressed all partial derivatives" is important in many fields of science and engineering, as it allows us to analyze and optimize multi-variable functions, such as those found in physics, economics, and statistics.

3. How do you calculate "expressed all partial derivatives"?

To calculate "expressed all partial derivatives", you take the partial derivative of the function with respect to each of its independent variables and arrange them into a matrix or vector, depending on the desired format. This can be done using the chain rule and basic rules of differentiation.

4. What is the difference between "expressed all partial derivatives" and "implicit differentiation"?

The main difference between "expressed all partial derivatives" and "implicit differentiation" is the number of variables involved. "Expressed all partial derivatives" deals with functions of multiple variables, while "implicit differentiation" deals with functions of a single variable.

5. In what real-world applications is "expressed all partial derivatives" commonly used?

"Expressed all partial derivatives" is commonly used in various fields such as physics, economics, engineering, and statistics. It is used to analyze and optimize multi-variable functions in real-world applications, such as in the design of structures, financial models, and physical systems.

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