How to Differentiate Exponential Functions with Multiple Variables?

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Homework Help Overview

The discussion revolves around differentiating an exponential function with multiple variables, specifically the function u = 2 (x - t² / 3)e^(t/3). Participants are exploring how to correctly apply differentiation techniques, including the chain rule and product rule, in this context.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants are attempting to differentiate the function with respect to both x and t, discussing the application of the chain rule and product rule. There are questions about the correctness of the derivatives calculated and the need for rewriting the function for clarity.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's attempts. Some guidance has been offered regarding the use of the chain rule and product rule, and there is acknowledgment of errors in the differentiation process that need to be addressed.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the extent of assistance they can provide to one another. There is an emphasis on ensuring that the derivatives are correctly calculated while considering the function's dependence on multiple variables.

andrey21
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Differentiate the following:

u = 2 (x-t2 / 3)et/3

Here is my attempt

I have to find du/dx and du/dt

du/dx = 2 (x-t2 / 3)et/3

du/dt = -4t/9 (x-t2 / 3)et/3
 
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It would help if you wrote u as 2xet/3 - (2/3)t2et/3. Since u is a function of both t and x, you will have to use the chain rule in your derivatives.

For example, if v = 3m2, then dv/dx = d/dx (3m2) = d/dm (3m2) (dm/dx) = 6m dm/dx.
 
Ok so from what you have said:

u = 2xet/3 - 2/3 t2et/3

du/dx = 2/ e t/3

du/dt = 2/3 xe t/3 - 4/9 t e t/3
 
Ok du/dx
There are errors in du/dt
 
Ah yes I need to adopt the product rule on:

-2/3 t2 e t/3
 

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