Differentiation of two similar systems

In summary, the conversation is about a student seeking help with understanding two different tasks involving differentiation. In the first system, the book gives the solution as f'(dY - dT), but does not specify which variable the derivative is in respect to. In the second system, the book gives the solution as f'(Y)*dY + f'(T)*dT + f'(r)*dr, with the symbols indicating the variables the derivatives are in respect to. The student's question is why the differentiation is different only for the C-equation in the two systems.
  • #1
monsmatglad
76
0

Homework Statement


Hi. i need help with understanding task with differentiation.
i have two separate tasks, and i need help understanding why the solutions differ somewhat.
system 1:
Y = C + I + G
C = f(Y-T)
I = h(r)
r = m(M)

system 2:
Y = C + I + G
C = F(Y,T,r)
I = f(Y,r)

in system 1. when differentiating system 1, the "C-equation", the book gives then answer f'(dY - dT),,,, the derivative is not specified to be in respect to Y or T.
in system 2, when differentiating the C-equation", the book gives the answer: f'(Y)*dY + f'(T)*dT + f'(r)*dr
the symbol in the parentheses are meant to tell in what respect the derivation is.
the question is, why are the differentiating ( only of the C-equation, i know how the rest) different?

Mons
2. Homework Equations

The Attempt at a Solution

 
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  • #2
found out on my own :)
 

1. What is differentiation of two similar systems?

Differentiation of two similar systems is a process of analyzing and understanding the differences between two systems that share similar characteristics or functions. It is commonly used in science to distinguish between closely related ideas, theories, or organisms.

2. Why is differentiation of two similar systems important?

Differentiation allows us to better understand the unique features of each system and how they differ from one another. This can lead to new discoveries and insights, and can also help us avoid confusion or misinterpretation of data.

3. How is differentiation of two similar systems performed?

Differentiation can be performed using various methods, depending on the specific systems being compared. Some common techniques include statistical analysis, comparative anatomy, and biochemical assays.

4. What are the benefits of differentiating two similar systems?

Aside from providing a better understanding of the systems being studied, differentiation can also help identify weaknesses or areas for improvement in one system compared to the other. This can lead to advancements and improvements in various fields of science.

5. Are there any limitations to differentiation of two similar systems?

One limitation of differentiation is that it may not always be possible to clearly distinguish between two systems, especially if they are very closely related. Another limitation is that differentiating systems can be a complex and time-consuming process, requiring extensive research and analysis.

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