- #1
hoch449
- 13
- 0
Homework Statement
Simplify the following two expressions:
[tex]y\frac{\partial}{\partial z}z\frac{\partial}{\partial x}[/tex]
[tex]z\frac{\partial}{\partial y}x\frac{\partial}{\partial z}[/tex]
The Attempt at a Solution
for the first one: [tex]y\frac{\partial}{\partial z}z\frac{\partial}{\partial x}[/tex]
[tex]\frac{\partial}{\partial z}z = 1[/tex]
so therefore [tex]y\frac{\partial}{\partial z}z\frac{\partial}{\partial x}= y(1)\frac{\partial}{\partial x}= y\frac{\partial}{\partial x}[/tex]
How come this is incorrect?
For the second one: [tex]z\frac{\partial}{\partial y}x\frac{\partial}{\partial z}[/tex]
I cannot write that [tex]z\frac{\partial}{\partial y}x\frac{\partial}{\partial z}= x\frac{\partial}{\partial z}z\frac{\partial}{\partial y}[/tex]
so therefore [tex]z\frac{\partial}{\partial y}x\frac{\partial}{\partial z}= zx\frac{\partial^2}{\partial y\partial z}[/tex]
The second one I believe is correct though..