Partial F/ Partial T F= (x,y) x and y = functs of s and t Only step 1 needed

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In summary, the conversation is about finding the partial derivative of f with respect to t, given the equations for x and y. The speaker initially suggests using a tree diagram to determine the partial derivatives, but then realizes that the s terms may not be necessary. They ask for guidance and eventually provide their new idea, which appears to be simpler.
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Yezman
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Wrong area sorry. Nub here! Can someone delete this.



If f(x,y) = Sqrt[x^4 + y] and x = s^2 + t^2 + 1 and y = t^2 +t*Cos(2s)

How do i find

Partial f
--------
Partial t


I made the tree diagram how f depends on x and y, which both depend on s and t... so on my test I said it was

(Partials of all of these)


f/x*x/s*x/t + f/y*y/s*y/t


Looking back now I wonder why I put the s's in there, seems like I don't need them. (this was from a recent test and we get to redo 1 problem). My new idea is

f/x*x/t + f/x*x/y ? That seems to simple though

Can someone here point in the right direction?

Thanks
 
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[tex]\frac{\partial f}{\partial t}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial t}[/tex]
 

1. What does Partial F/Partial T mean in this context?

Partial F/Partial T refers to the partial derivative of the function F with respect to the variable T. It represents the rate of change of the function F as T changes, while holding all other variables constant.

2. What does the notation F= (x,y) x and y = functs of s and t mean?

This notation indicates that the function F is a function of both x and y, where x and y are also functions of the variables s and t. In other words, the value of F depends on the values of both x and y, which in turn depend on the values of s and t.

3. Why is only step 1 needed in this context?

In this context, only step 1 is needed because it refers to finding the partial derivative of F with respect to T. If additional information or calculations are needed, then additional steps may be required.

4. What is the purpose of finding the partial derivative in this situation?

The purpose of finding the partial derivative is to understand how a specific variable (in this case, T) affects the overall function F. It allows for a more in-depth analysis of the function and can be useful in making predictions or optimizing the function.

5. How does this concept relate to real-world applications?

Partial derivatives are commonly used in physics, engineering, economics, and other fields to model and analyze systems that involve multiple variables. For example, in physics, partial derivatives are used to calculate rates of change in thermodynamics and fluid dynamics. In economics, they can be used to determine the impact of one variable on a larger system, such as the effect of interest rates on the economy.

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