First Order Partial Derivatives of a Function

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Homework Help Overview

The discussion revolves around finding the first order partial derivatives of the function f(x,y) = ln|(x+√(x²+y²))/(x-√(x²+y²))| at the point (4,3). Participants express challenges in simplifying the function to facilitate the calculation of the partial derivatives.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various simplification techniques, including the use of logarithmic properties and division of terms. There are questions about the correctness of expressions and the impact of typos on the simplification process. Some participants suggest directly computing the partial derivatives from the current form of the function.

Discussion Status

The discussion is ongoing, with participants exploring different methods to simplify the function and clarify their understanding of the derivative process. Some have provided guidance on potential approaches, while others express confusion about specific algebraic manipulations and derivative rules.

Contextual Notes

There are indications of typos and misunderstandings regarding the application of logarithmic identities and derivative rules. Participants are also navigating the complexities of differentiating functions that involve both x and y variables.

  • #31
ok once again thanks Voko you have been brilliant!

f(x)= [1+(x^2+y^2)^{-1/2}(x)] [\frac{1}{x+\sqrt{x^2+y^2}} - \frac{1}{x-\sqrt{x^2+y^2}}]

So this is written correctly then?
 
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  • #32
Again, the second term is incorrect. You cannot go from (-a)(b) to -(-ab), but that's what you insist on doing. (-a)(b) = -(ab).
 

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