How to calculate jacobian matrix

[NapDynamite]

Refering to my last message, I need to take partial derivative of OBJECTIVE FUNCTION with respect to QUATERNION. I need to derivate each entry of OBJECTIVE FUNCTION with respect to every entry of QUATERNION according to the definition of Jacobian Matrix. 

[BoKnows]

Have you tried using the Partial Derivatives VI included in the math palette?  Once you can calculate a partial derivative, the rest of your code should just be manipulating the inputs and outputs to get the desired values.