Math Problem Solver

The function (f: \mathbb{R}^2 \to \mathbb{R)) be defined as[

f(x, y) = \begin{cases) \frac{x^2 y^2-\sin(y^4)){x^2 + y^2} + \in(1 + x^2 + y^2), & \text{if } (x, y) \neq (0, 0), \ a, & \text{if) (x, y) = (0, 0), \end{cases) and (g(x, y) = f(x, y)^2 + \frac{e^{-x^2-y^2)}{x^2+y^2+1)) for ((x, y) \neq (0, 0)), with (g(0, 0) = b).Compute the Hessian matrix of (g(x, y) at ((0, 0)).[ f(x, y) = \begin{cases) \frac{x^2 y^2-\sin(y^4)){x^2 + y^2} + \in(1 + x^2 + y^2), & \text{if } (x, y) \neq (0, 0), \ a, & \text{if) (x, y) = (0, 0), \end{cases) and (g(x, y) = f(x, y)^2 + \frac{e^{-x^2-y^2)}{x^2+y^2+1)) for ((x, y) \neq (0, 0)), with (g(0, 0) = b).Compute the Hessian matrix of (g(x, y) at ((0, 0)).