19. I.1 Generalized Derivatives

Condition: show that the next display is differentiated and find its strong derivative: \ [f: \ mathb {r} _ {2} {3} \ rightarrow {r} _ {2}^{3}, \ quad \ left \ {\ begin {array} {c} y_ {1} = 2 x_ {1} {2}+x_ {1} x_ {2}} -x_ {1} x_} \\ y_ {2} = x_ {1} {1} {1} {1} {1} x_ {2} -3 x_ {2}^{2}+x_ {1} x_ {3}^{2} \\ y_ {3} = 2 x_ {1} {2} x_^{2} -4 x_ {2} {2} x_ {3} x_ {3} x_ {3} x_ {3} x_ {3} x_ \ end {Array} \ Right. \] at the point \ ((1,1,1) \).