Hessian Calculator

Find the hessian matrix of the function $x^{3} + 4 x y^{2} + 5 y^{3} - 10$ with respect to $x$, $y$.

The entry at row $i$, column $j$ of the Hessian matrix is the partial derivative of the function with respect to the $i$-th and $j$-th variables.

$H_{11} = \frac{d^{2}}{dx^{2}} \left(x^{3} + 4 x y^{2} + 5 y^{3} - 10\right) = 6 x$ (for steps, see partial derivative calculator).

$H_{12} = \frac{d^{2}}{dydx} \left(x^{3} + 4 x y^{2} + 5 y^{3} - 10\right) = 8 y$ (for steps, see partial derivative calculator).

$H_{21} = \frac{d^{2}}{dxdy} \left(x^{3} + 4 x y^{2} + 5 y^{3} - 10\right) = 8 y$ (for steps, see partial derivative calculator).

$H_{22} = \frac{d^{2}}{dy^{2}} \left(x^{3} + 4 x y^{2} + 5 y^{3} - 10\right) = 2 \left(4 x + 15 y\right)$ (for steps, see partial derivative calculator).

Thus, $H = \left[\begin{array}{cc}6 x & 8 y\\8 y & 2 \left(4 x + 15 y\right)\end{array}\right]$.

$H = \left[\begin{array}{cc}6 x & 8 y\\8 y & 2 \left(4 x + 15 y\right)\end{array}\right]$A