- #1
newguy1234
- 13
- 0
Hello I am trying to figure out the second derivative of
[tex] \frac{\partial^2 z}{\partial x^2}[/tex] and [tex] \frac{\partial^2 z}{\partial t^2}[/tex]
z(u) and u=x-vt
i found the first derivate of [tex] \frac{\partial z}{\partial x}[/tex] to be
[tex] \frac{\partial z}{\partial x}[/tex]= [tex] \frac{\partial z}{\partial u}[/tex] * [tex] \frac{\partial u}{\partial x}[/tex] = [tex] \frac{\partial z}{\partial u}[/tex] *1
and
[tex] \frac{\partial z}{\partial t}[/tex] = [tex] \frac{\partial z}{\partial u}[/tex] * [tex] \frac{\partial u}{\partial t}[/tex]= [tex] \frac{\partial z}{\partial u}[/tex]*v
after this i am clueless on how to compute
([tex] \frac{\partial }{\partial t}[/tex])[tex] \frac{\partial z}{\partial u}[/tex]*v
and
([tex] \frac{\partial }{\partial x}[/tex])[tex] \frac{\partial z}{\partial u}[/tex]*1
i am new here am hoping to receive some help i will greatly appreciate it!
[tex] \frac{\partial^2 z}{\partial x^2}[/tex] and [tex] \frac{\partial^2 z}{\partial t^2}[/tex]
z(u) and u=x-vt
i found the first derivate of [tex] \frac{\partial z}{\partial x}[/tex] to be
[tex] \frac{\partial z}{\partial x}[/tex]= [tex] \frac{\partial z}{\partial u}[/tex] * [tex] \frac{\partial u}{\partial x}[/tex] = [tex] \frac{\partial z}{\partial u}[/tex] *1
and
[tex] \frac{\partial z}{\partial t}[/tex] = [tex] \frac{\partial z}{\partial u}[/tex] * [tex] \frac{\partial u}{\partial t}[/tex]= [tex] \frac{\partial z}{\partial u}[/tex]*v
after this i am clueless on how to compute
([tex] \frac{\partial }{\partial t}[/tex])[tex] \frac{\partial z}{\partial u}[/tex]*v
and
([tex] \frac{\partial }{\partial x}[/tex])[tex] \frac{\partial z}{\partial u}[/tex]*1
i am new here am hoping to receive some help i will greatly appreciate it!