- #1
petertheta
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I have a question but have not seen an example or find anything in my textbooks so would love some advice on how to understand the problem.
Its a theory question on partial derivatives of the second order...
T=T(x,y,z,t) with x=x(t), y=y(t), z=z(t).
Find the second derivative of T wrt t
So, first find the first derivative to give:
[tex]\frac{dT}{dt} = \frac{\partial T}{\partial x}\frac{dx}{dt} +\frac{\partial T}{\partial y}\frac{dy}{dt}+\frac{\partial T}{\partial z}\frac{dz}{dt}+\frac{\partial T}{\partial t}[/tex]
So I know the second derivative will be:
[tex]\frac{d}{dt}\left(\frac{dT}{dt}\right)[/tex]
So now my question. How do i take derivatives of products of mixed derivatives and write it in a correct manner, albeit a theoretical one.
Your help means a lot.
PT
Its a theory question on partial derivatives of the second order...
T=T(x,y,z,t) with x=x(t), y=y(t), z=z(t).
Find the second derivative of T wrt t
So, first find the first derivative to give:
[tex]\frac{dT}{dt} = \frac{\partial T}{\partial x}\frac{dx}{dt} +\frac{\partial T}{\partial y}\frac{dy}{dt}+\frac{\partial T}{\partial z}\frac{dz}{dt}+\frac{\partial T}{\partial t}[/tex]
So I know the second derivative will be:
[tex]\frac{d}{dt}\left(\frac{dT}{dt}\right)[/tex]
So now my question. How do i take derivatives of products of mixed derivatives and write it in a correct manner, albeit a theoretical one.
Your help means a lot.
PT
Homework Statement
Homework Equations
The Attempt at a Solution
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