Partial Derivatives of Multivariable Functions

In summary, the conversation involved discussing a problem involving the function T(x,y,z,t) with the given equation. The speaker took the partial derivative with respect to x and broke the problem into two parts. They determined that the left side was -2y^2 and used the chain rule to find the right side, which was -sin(5x-.75t)5. They then asked for confirmation on their final answer and mentioned a possible error with a TI calculator they were using. The other person confirmed that their answer was correct and asked about the voyage 200, which is a TI calculator.
  • #1
badtwistoffate
81
0
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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  • #2
So the final answer for [itex]\partial T/\partial x[/itex] is what according to you?
 
  • #3
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:
  • #4
That's the correct answer. What's a voyage 200?
 
  • #5
its a TI calculator that does alot.
 

1. What is a partial derivative?

A partial derivative is a mathematical concept used to describe how a function changes with respect to one of its variables while holding all other variables constant.

2. Why are partial derivatives important?

Partial derivatives are important because they allow us to analyze the behavior of multi-variable functions and understand how small changes in one variable affect the overall function.

3. How do you calculate a partial derivative?

A partial derivative is calculated by taking the derivative of a multi-variable function with respect to one variable while holding all other variables constant.

4. What is the difference between a partial derivative and a total derivative?

A partial derivative only considers the effect of one variable on a function, while a total derivative takes into account the effects of all variables on a function.

5. How are partial derivatives used in real-world applications?

Partial derivatives are used in various fields such as physics, engineering, economics, and statistics to model and analyze complex systems. They are also used in optimization problems to find the maximum or minimum of a function.

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