How to Find Jacobian of functions given below

Question : Find Jacobian of functions given below \[f(x,y)=y\left(1-\left(x^2+y^2\right)\right) , g(x,y)=x\left(1-\left(x_2+y^2\right)\right) \] Solution :given functions \[f(x,y)=y\left(1-\left(x^2+y^2\right)\right) , g(x,y)=x\left(1-\left(x_2+y^2\right)\right) \] Their first order partial derivatives are \frac{\partial f}{\partial x} = -2xy\]\[\frac{\partial f}{\partial y} = -2y^2\]\[\frac{\partial g}{\partial x} = -2x^2\]\[\frac{\partial g}{\partial y}…

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