Changes

*<math>f_2(x_1,x_2) = \frac{\partial f(x_1,x_2)}{\partial x_2} = \frac{- 2 x_1^3 x_2}{(1+x_2^2)^2}</math>

*<math>f_2(x_1,x_2) = \frac{\partial f(x_1,x_2)}{\partial x_2} = \frac{- 2 x_1^3 x_2}{(1+x_2^2)^2}</math>

Note that the two partial derivatives <math>f_1(x_1,x_2)</math> and <math>f_2(x_1,x_2)</math> in example are again differentiable functions of <math>x_1</math> and <math>x_2</math>, so higher derivatives can be calculated:

Note that the two partial derivatives <math>f_1(x_1,x_2)</math> and <math>f_2(x_1,x_2)</math> in this  example are again differentiable functions of <math>x_1</math> and <math>x_2</math>, so higher derivatives can be calculated:

*<math>f_{11}(x_1,x_2) = \frac{\partial^2 f(x_1,x_2)}{\partial x_1 \partial x_1}\;</math><math> = \frac{6 x_1}{1+x_2^2}</math>

*<math>f_{11}(x_1,x_2) = \frac{\partial^2 f(x_1,x_2)}{\partial x_1 \partial x_1}\;</math><math> = \frac{6 x_1}{1+x_2^2}</math>