Solution
= Solution
The <derivative> is represented by the <gradient>, and the <Hessian matrix> contains the second partial <derivatives>:
$$
\boxed{\nabla f(x,y)=\begin{pmatrix}4x^3-4y\\4y-4x\end{pmatrix},\qquad H(f)(x,y)=\begin{pmatrix}12x^2&-4\\-4&4\end{pmatrix}.}
$$
Equivalently the <derivative> as a linear map is $Df(x,y)(u,v)=(4x^3-4y)u+(4y-4x)v$.