Total differentiation

[Xatta]

Hi!

I have been working on partial differentiation too long, and have forgotten the basics of total differentiation..!

I would really appreciate if someone could help me by explaining how this equation is solved (if you could write how you split up the expression, and the solving of it...)

by solving the two equations: [attachment=1:31bq43ar]1-1.JPG[/attachment:31bq43ar], it can be shown that:
[attachment=0:31bq43ar]1-2.JPG[/attachment:31bq43ar]

The problem is to solve: dp2/dx1 = ?
Can anyone help me?

 

[tkhunny]

Your question seems to be a little spread out, as if it really has no direction.

1) One would have to know more about all the mystery parameters/variables/constants/whatever-they-are. c = ??, t = ??, \(\displaystyle \tau\) = ?? Most Important, are they also functions of one of the 'x's or are they constant?

2) Written out in this form, \(\displaystyle p_{2} = c(1+\tau) + \frac{t}{3}(3 - 4x_{1} - 2x_{2} + x_{1}^{2} - x_{2}^{2})\), it is very simply, assuming you have answered #1 favorably.