Partial Derivatives of Multivariable Functions

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SUMMARY

The discussion focuses on calculating the partial derivative of the multivariable function T(x,y,z,t) = -2xy² + e^(-3z)cos(5x - 0.75t) with respect to x. The correct partial derivative is confirmed as ∂T/∂x = -2y² - 5e^(-3z)sin(5x - 0.75t). The participant initially struggled with applying the chain rule for the right side of the function but ultimately received confirmation of their answer. A TI Voyage 200 calculator was mentioned as a tool for verification.

PREREQUISITES
  • Understanding of multivariable calculus
  • Familiarity with partial derivatives
  • Knowledge of the chain rule in differentiation
  • Experience using TI calculators, specifically the Voyage 200
NEXT STEPS
  • Study the application of the chain rule in multivariable functions
  • Learn how to compute partial derivatives for functions of multiple variables
  • Explore the capabilities of the TI Voyage 200 calculator for calculus
  • Review examples of partial derivatives in physics and engineering contexts
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Students and professionals in mathematics, engineering, and physics who are working with multivariable functions and need to understand partial derivatives.

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 \partial T/\partial x 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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