Partial derivative of a total derivative

[halley00]

Hi,

So, in order to calculate a Jacobian, I need to evaluate a partial derivative of a total derivative, i.e.
Let's say I have a function f(x), how do I calculate something like: ∂(df/dx)/∂f?

 

[jedishrfu]

Is this an actual example or something you just thought of?

I can see you using the Jacobian to convert an integral from say XY cartesian coordinates to polar coordinates but not using f(x) by itself.

integral ( f(x,y) dx dy) ---> integral (f(r,phi) Jacobian(r,phi) dr dphi)

So you'd start with x=r * cos(phi) and y=r * sin(phi) and compute the Jacobian
and then you'd convert f(x,y) to f(r,phi)

https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

Here's a short video tutorial on the Jacobian:

 

[halley00]

Thank you for your reply. It is an actual example. I have to solve a system of differential equations using Newton-Raphson method, so, let's say I have a function: f1(y1(x1),y2(x1,x2)) = 0, with something like f1 =dy1/dx1 + something else. Then to construct the Jacobian I'll need to evaluate ∂f1/∂y1, which will lead to ∂(dy1/dx1)/∂y1. Any leads?

 

[jedishrfu]

Thank you for your reply. It is an actual example. I have to solve a system of differential equations using Newton-Raphson method, so, let's say I have a function: f1(y1(x1),y2(x1,x2)) = 0, with something like f1 =dy1/dx1 + something else. Then to construct the Jacobian I'll need to evaluate ∂f1/∂y1, which will lead to ∂(dy1/dx1)/∂y1. Any leads?

Remember the chain rule?

∂f1/∂y1 * ∂y1/∂x1 = ∂f1/∂x1