How do I solve this first order partial derivative problem?

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Discussion Overview

The discussion revolves around solving a first order partial derivative problem involving the function z = 3x^2*y^3*e^(5x-3y) + ln(2x^2 + 3y^3). Participants are seeking clarification on the process of finding partial derivatives with respect to x and y.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to approach the problem and mentions the need to find Fx(x,y) while treating one variable as a constant.
  • Another participant suggests that to find Fx, one could replace y with a constant value (like a or pi) and then differentiate with respect to x.
  • Some participants discuss the method of treating the non-differentiated variable as a constant and differentiating normally, with one noting that setting the variable to a specific number might confuse others.
  • There is a reiteration that the process involves fixing one variable and differentiating with respect to the other.

Areas of Agreement / Disagreement

Participants generally agree on the method of treating one variable as a constant while differentiating with respect to the other, but there is some confusion regarding the approach of substituting specific values for clarity.

Contextual Notes

Some participants express uncertainty about the clarity of the substitution method and its potential to confuse others, indicating a need for clearer communication of the process.

Spectre32
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We went over this breifly in class and I'm confused on it. Were doing first order only and this is the problem: z = 3x^2*y^3*e^(5x-3y) + ln(2x^2 + 3y^3) I know your susposed to Fx(x,y) and treat X or Y as a constant, depending, upon how you want to start, but I'm still unclear as to how to solve this.

Thanks for the help.
 
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Well you know how to find an ordinary derivative, so if you need to get Fx, replace y by something else, like a or 17 or pi or whatever, then find the x derivative.
 
So you just single each variable out and that's it?
 
You treat the variable you are not differentiating with respect to as any other constant, and then you differentiate normally.

Setting the variable equal to 17 or pi or something would probably confuse lots of people, though...

cookiemonster
 
yeah i was confused by that.
 
Spectre32 said:
So you just single each variable out and that's it?

yeah that's it. Fix one (pretend it's constant), differentiate with respect to the other.
 

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