Partial Derivatives of Multivariable Functions

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Homework Help Overview

The discussion revolves around finding the partial derivative of a multivariable function T(x,y,z,t) = -2xy^2 + e^(-3z)cos(5x - 0.75t) with respect to x. Participants are exploring the application of differentiation rules, particularly the chain rule and product rule, in this context.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to differentiate the function by breaking it into parts and applying the chain rule. Some participants question the correctness of the derivative obtained and express uncertainty about their calculations.

Discussion Status

Participants are actively discussing the steps involved in finding the partial derivative, with one individual expressing doubt about their answer and seeking confirmation. There is an exchange of information regarding tools used for verification, indicating a collaborative effort to clarify the solution.

Contextual Notes

One participant mentions using a TI calculator for verification, which raises questions about reliance on technology for checking mathematical work. There is also an indication of uncertainty regarding the correctness of the derivative, suggesting that participants are grappling with the application of differentiation rules.

badtwistoffate
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Ok i got this problem...
T(x,y,z,t)= -2xy^2+e^(-3z)cos(5x-.75t)
taking the partial derivative with respect to x first, so i break the problem apart with the left and right sign of the addition side

so i get...
-2y^2 for the left side and then am stubling on the right side, I am think just chain rule since e^(-3z) is constant right? so I get -sin(5x-.75t)5 from the right side.

any help
 
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So the final answer for [itex]\partial T/\partial x[/itex] is what according to you?
 
its -2y^2-e^(-3z)*sin(5x-.75t)5 I THINK, butttt... i have a voyage 200 near me and when i check it, its giving me a error and I don't trust myself enough to think its right...
 
Last edited:
That's the correct answer. What's a voyage 200?
 
its a TI calculator that does a lot.
 

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