722.sagews

f=x^2*sin(y)

f.hessian()

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rr} 2 \, \sin\left(y\right) & 2 \, x \cos\left(y\right) \\ 2 \, x \cos\left(y\right) & -x^{2} \sin\left(y\right) \end{array}$$\right)

f.gradient()

\newcommand{\Bold}[1]{\mathbf{#1}}\left(2 \, x \sin\left(y\right),x^{2} \cos\left(y\right)\right)

f.hessian()^-1

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rr} -\frac{x^{2} \cos\left(y\right)^{2}}{{(x^{2} \sin\left(y\right) + 2 \, \frac{x^{2} \cos\left(y\right)^{2}}{\sin\left(y\right)})} \sin\left(y\right)^{2}} + \frac{1}{2} \, \frac{1}{\sin\left(y\right)} & \frac{x \cos\left(y\right)}{{(x^{2} \sin\left(y\right) + 2 \, \frac{x^{2} \cos\left(y\right)^{2}}{\sin\left(y\right)})} \sin\left(y\right)} \\ \frac{x \cos\left(y\right)}{{(x^{2} \sin\left(y\right) + 2 \, \frac{x^{2} \cos\left(y\right)^{2}}{\sin\left(y\right)})} \sin\left(y\right)} & -\frac{1}{{(x^{2} \sin\left(y\right) + 2 \, \frac{x^{2} \cos\left(y\right)^{2}}{\sin\left(y\right)})}} \end{array}$$\right)

f.hessian()^-1*f.gradient()

\newcommand{\Bold}[1]{\mathbf{#1}}\left(-{(2 \, \frac{x^{2} \cos\left(y\right)^{2}}{{(x^{2} \sin\left(y\right) + 2 \, \frac{x^{2} \cos\left(y\right)^{2}}{\sin\left(y\right)})} \sin\left(y\right)^{2}} - \frac{1}{\sin\left(y\right)})} x \sin\left(y\right) + \frac{x^{3} \cos\left(y\right)^{2}}{{(x^{2} \sin\left(y\right) + 2 \, \frac{x^{2} \cos\left(y\right)^{2}}{\sin\left(y\right)})} \sin\left(y\right)},\frac{x^{2} \cos\left(y\right)}{{(x^{2} \sin\left(y\right) + 2 \, \frac{x^{2} \cos\left(y\right)^{2}}{\sin\left(y\right)})}}\right)