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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?

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- Thread starter halley00
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- #1

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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?

- #2

jedishrfu

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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:

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:

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- #4

jedishrfu

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Remember the chain rule?

∂f1/∂y1 * ∂y1/∂x1 = ∂f1/∂x1

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