Finding the Gradient using Quotient Rule

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    Gradient quotient
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Homework Help Overview

The discussion revolves around finding the gradient of a function F(s,t) defined in terms of another function f(x,y) and the variables x and y, which are expressed as functions of s and t. The subject area includes calculus, specifically the application of the chain rule and quotient rule in partial derivatives.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the chain rule for partial derivatives and explore the relationship between the variables involved. There is a mention of the specific formula for calculating the partial derivative of F with respect to s.

Discussion Status

The conversation includes an initial request for guidance, followed by a clarification about the chain rule. One participant confirms they have successfully completed the problem after receiving assistance, indicating a productive exchange of ideas.

Contextual Notes

There is an indication of uncertainty at the beginning of the discussion, with the original poster expressing difficulty in starting the problem. The conversation also reflects a collaborative effort to clarify the application of calculus concepts without providing a complete solution.

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Find the gradient of F(s,t) = f(x(s,t), y(s,t)) where f(x,y) = y/x x = s^2 + t^2 y = s^2 - t^2.

I'm not sure how to even start the problem. Could someone point me in the right direction?
 
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Do you know the chain rule for partial derivatives?
 
Does it have something to do with this:

\frac{\partial F}{\partial s} = \frac{\partial F}{\partial x}\frac{\partial x}{\partial s} + \frac{\partial F}{\partial y} \frac{\partial y}{\partial s}
 
Yes, now DO it!
 
Already did, and got the correct answer, thank you.
 

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