Does anybody have the proof of 9a,b in "Session-43-Clearer Notation-Notes" ? The one called chain rule for partial derivatives of a function of 4 variables x,y,z,t ?
$$(\delta(x)/\delta(y) )_z*(\delta(y)/\delta(t) )_z=(\delta(x)/\delta(t) )_z$$

Question

anonymous · Answer

attachment

anonymous · Answer

$$(\delta(x)/\delta(y) )_z*(\delta(y)/\delta(t) )_z=(\delta(x)/\delta(t) )_z$$

baru · Answer

if i remember correctly,
these are not exactly rules for functions of 4 variables...

these rules are valid for this situation:
among x,y,z,t
only two can be independently chosen, 
as in if we choose values for x and t, then the values of y and z are automatically decided.

consequently,
any three variables are connected by some equation:
ex: f(y,z,t)= c
     g(x,z,t)=k

use the total differential on  f( ) and g( ) i just mentioned, and you will be able to arrive at the rules

baru · Answer

*c and k are constants