I am trying to calculate the Jacobian of a function but I don't know whether I got it right. The function is $$ f(x)=\frac{F}{V}\cdot(x_{in}-x)+\beta\cdot(k_0\cdot e^{-E_a/x})\cdot(C_{A,in}+\frac{1}{\beta}\cdot(x_{in}-x))\cdot(C_{B,in}+\frac{2}{\beta}\cdot(x_{in}-x)) $$ where x is a scalar variable
Using the chain rule I calculated the Jacobian to be $$ J=-\frac{F}{V}+\frac{\beta\cdot k_0\cdot E_a\cdot e^{-E_a/x}}{x^2}\cdot(-\frac{1}{\beta})\cdot(-\frac{2}{\beta}) $$
But I am pretty sure I got a wrong result by doing something wrong using the chain rule. Can anyone help me out here?
Thanks