Question

Someone help me, please
find the jacobian matrix of f(x,y) = sin(x^2+y^3)

Answer 1

It's easy to see that \(J_{x,y}=( 2xcos(x^2+y^3), 3y^2 cos(x^2+y^3))\)

Answer 2

it looks good to me

Answer 3

All I need is the formal form of Jacobian, it looks like
\(J_{x,y}=\left[\begin{matrix}\dfrac{\partial f}{\partial x}&\dfrac{\partial f}{\partial y}\end{mtarix}\right]\)