Second Derivative Rule

1. Apr 8, 2014

chicago77

So this is a theoretical question I am not sure about with partial derivatives.

Say we have function x(i,j) with a=dx/di and b=dx/dj

Now is this logical when the cross derivatives are required to be equal?

db/da --> substitute b
= d^2x/((d^2x/di)dj)
=di/dj

Is this allowed?

2. Apr 8, 2014

Staff: Mentor

Right off the bat I'm not following this. This says you are taking the (partial) derivative with respect to dx/dj, which makes not sense at all.

A small part of my difficulty is with your notation - dx/di - which is supposed to be the partial derivative of x with respect to i.
Presumably i and j (which are really bad choices for the names of variables) are independent variables, so you wouldn't ordinarily take the derivative (partial or otherwise) of one with respect to the other.

3. Apr 8, 2014

chicago77

nvm I have solved this with a lagrangian.

Last edited: Apr 8, 2014