Find the gradient vector fx fy and the Hessian matrix of the

Find the gradient vector [f_x, f_y] and the Hessian matrix of the fuiictiou f(x, y) = x^3 In y + 6x^2 + e^2x y. Here Hessian matrix is the Jacobian matrix of the gradient, i.e. [f_xy f_xy f_yx f_yy]

Solution

f_x = 3x².ln(y) + 12xy³ + 2ye^2x

f_y = ( (x³ + 18x²y³)/y )  + e^2x

f_xx = 4ye^2x + 12y³ + 6x.ln(y)

f_xy = ( (3x² + 36xy³)/y )  + 2e^2x

f_yx = ( (3x² + 36xy³)/y )  + 2e^2x

f_yy = 36x²y - ( x³/y² )