Consider f: C{0} C by (2) == / (a) Writing z = x+iy find the...

 

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Consider f: C\{0} → C by ƒ(2) == / (a) Writing z = x+iy find the real and imaginary u: R²\{(0,0)} → R and v R²\{(0,0} → R parts of f. (b) Compute the partial derivatives: du du dv Əv and 1 дл' ду Әх ду (c) Compute the second homogeneous partial derivatives: P²u Pu ²v and Ər²¹ Əy²¹ Ər²¹ dy² Consider f: C\{0} → C by ƒ(2) == / (a) Writing z = x+iy find the real and imaginary u: R²\{(0,0)} → R and v R²\{(0,0} → R parts of f. (b) Compute the partial derivatives: du du dv Əv and 1 дл' ду Әх ду (c) Compute the second homogeneous partial derivatives: P²u Pu ²v and Ər²¹ Əy²¹ Ər²¹ dy²