Help with multivariable calculus and heat equation? (true/false)

[Davidpersiani]

Please help me with these problems, especially number 3. I know the first one is false.

 

[Deleted member 4993]

Please help me with these problems, especially number 3. I know the first one is false.

Calculate U_t and calculate U_xx and check the equation

 

[Davidpersiani]

I don't know how to do that. How do I do it?

 

[Davidpersiani]

And what about 2 and 4? Do you just plug the numbers in?

 

[Deleted member 4993]

I don't know how to do that. How do I do it?

U_t is the partial derivative U with respect to 't'.

Are you saying you have not been taught to do that?

 

[Davidpersiani]

No, I was never taught. How would I calculate it?

 

[Deleted member 4993]

No, I was never taught. How would I calculate it?

In

https://www.freemathhelp.com/forum/threads/help-with-multivariable-function.119305/

You said "I already know the domain and the gradient" of a given function?

How did you calculate gradient without knowing partial (differentiation) derivative?

 

[Davidpersiani]

I calculated the gradient by taking the partial derivative. But I don't know the heat equation notation. Would I calculate the partial derivative of t? So -8e^(-8t) * sin(Constant) *0 so it would be zero?