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10.6.3 Analytic functions
Problem: Prove that function
f
(
z
)
=
u
(
x
,
y
)
+
i
v
(
x
,
y
)
is differentiable on the entire complex plane and find its derivative
f
′
(
z
)
.
f
(
z
)
=
(
3
x
3
−
6
x
y
2
+
2
x
2
−
2
y
2
−
3
x
+
1
)
+
+
i
(
6
x
2
y
−
2
y
3
+
4
x
y
−
3
y
)
.
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