Another question thrown at you

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Homework Help Overview

The discussion revolves around a problem in multivariable calculus involving the differentiation of a function defined as F(x,y) = f(x + g(y)), where f and g are twice differentiable functions. The goal is to show a specific relationship between the first and second order partial derivatives of F.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the differentiation of the function F and discuss rewriting the derivatives in terms of the chain rule. Some express uncertainty about their progress, while others indicate they may have found a solution.

Discussion Status

The discussion includes attempts to manipulate the derivatives of F and some participants express feelings of being stuck or uncertain. There is a mix of progress and requests for further assistance on remaining questions.

Contextual Notes

Participants mention constraints related to posting multiple questions and express concerns about potential repercussions for doing so. There is an emphasis on the manipulation of derivatives and the application of the chain rule in the context of the problem.

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I think I'll get banned soon posting multiple questions at the same time, but allow me to continue,
if f,g:R-->R both of class C2(differentiable twice)
Define F(x,y)=f(x+g(y))
Show that (DxF)(DxDyF)=(DyF)(D^2xF) where D^2xF is second order partial derivative with respect to x
I'm dying here...
 
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umm... forget it I think I can do this one.. lol
 
Umm... I'm stuck..
 
Rewrite [itex]F_x(x,y)[/itex] and [itex]F_{yx}(x,y)[/itex] in terms of derivatives of [itex]f(x+g(y))[/itex] and [itex]g(y)[/itex] (the rest is straightforward manipulation, using the chain rule).
 
Yes! It did work! Thank you!
Now please the remaining questions I posted, could anyone please answer??
 

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