Find the gradient of f(x,y). f(x,y)=(x^2)e^-2y

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Discussion Overview

The discussion focuses on finding the gradient of the function f(x,y) = (x^2)e^-2y. Participants are seeking clarification and verification of their calculations related to this mathematical problem.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents their calculated gradient as <2xe^-2y, 2x-2e^-2y> and expresses uncertainty about its correctness.
  • Another participant asserts the correct form of the gradient as grad f = fx(x,y)i + fy(x,y)j, providing fx(x,y) = (2x)e^-2y and fy(x,y) = (-2*2x)e^-2y.
  • A third participant challenges the calculation of fy, stating that the derivative of e^-2y with respect to y should yield fy = -2x^2e^-2y, leading to a gradient of <2xe^-2y, -4xe^-2y>.
  • The third participant also points out potential typos in the first participant's expression, suggesting that it may have been a result of carelessness.

Areas of Agreement / Disagreement

There is disagreement regarding the correct calculation of the gradient, particularly the fy component. Multiple competing views remain, and the discussion is unresolved.

Contextual Notes

Participants have not reached consensus on the correct form of the gradient, and there are indications of potential errors in the expressions provided.

ffrpg
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Here's the problem. Find the gradient of f(x,y). f(x,y)=(x^2)e^-2y.


I don't have the solution to this and I need to know if I got the right gradient (I have more problems that depend on this gradient, points on it). I ended up getting, gradient f=<2xe^-2y, 2x-2e^-2y>. I don't think it's right, but can someone help me out here?
 
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No.
grad f= fx(x,y)i + fy(x,y)j
fx(x,y)=(2x)e-2y
fy(x,y)=(-2*2x)e-2y
 
Sorry, Stephen, you have fy wrong.

The derivative of e-2y with respect to y is -2 e-2y The other factor, x2 is independent of y so treat it like a constant fy= (x2)(-2e-2y)= -2x2e-2y.

The gradient of 2xe-2y is the vector <2x e-2y, -4xe-2y>.

What ffrpg wrote: f=<2x^e-2y, 2x-2e^-2y> may be typos or just carelessness: x^e-2y doesn't make much sense and in "2x-2..." you MEANT (2x) times (-2), not 2x subtract 2...
 
Ah yes. Where is my head?
 

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