Question

Wanna check something, I'm typing it give me a second

Answer 1

:O .. i posted this to get the notification when ur done lols

Answer 2

Given:
\[f(x,y),x(u,v),y(u,v)\]
Find:
\[\frac{\partial^2f}{\partial v \partial u}\]
I did:
\[\frac{\partial f}{\partial u}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial u}\]
Then:
\[\frac{\partial^2 f}{\partial v \partial u}=\frac{\partial}{\partial v}(\frac{\partial f}{\partial u})\]
Then:
\[\frac{\partial}{\partial x}\frac{\partial x}{\partial v}\frac{\partial f}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial}{\partial y}\frac{\partial y}{\partial v}\frac{\partial f}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial f}{\partial x}\frac{\partial}{\partial v}\frac{\partial x}{\partial u}+\frac{\partial}{\partial x}\frac{\partial x}{\partial v}\frac{\partial f}{\partial y}\frac{\partial y}{\partial u}+\frac{\partial f}{\partial y} \frac{\partial}{\partial y}\frac{\partial y}{\partial v}\frac{\partial y}{\partial u}+\frac{\partial f}{\partial y}\frac{\partial}{\partial v}\frac{\partial y}{\partial u}\]

Answer 3

The last bit should be:
\[\frac{\partial f}{\partial y}\frac{\partial}{\partial y}\frac{\partial y}{\partial u}\]

Answer 4

My bad, bad typing, the middle of the 3 above should be \[\frac{\partial}{\partial v}\]