المحاضرة السابعة عشر

56
( Derivative )
z w = f(z) ?
z? z?
z? z?
z0 ( Differentiable ) f
z0 f
z0 f z0 f
Ex : let f(z) = ?z?2 is cont. fun. But isn t Diff.
( differentiation Formulas )
z
g (z) f (z) n k
z
?
?
? z z
f z f z f z
z z ?
?
? ?
?
( ) lim ( ) ( )
z
f z f z z f z
z ?
? ? ?
? ?
? ?
( ) ( )
( ) 0
0 lim ?
57
1) = 0
2) = 1
3) = k
4) = ±
5) = f (z) { } + { . g (z) }
6) { } =
7) { f(z)}n = n { f(z)}n-1 .
1
f (z) = z6 + 2z3 - 3
f (z) =
2
f (z) = 3z2 – z-1 , z0 = i
f (z) = z2 + 1 , z0 =
d (k)
dz
d (z)
dz
d ( k f(z) )
dz
d (f (z))
dz
d { f(z) ± g(z) }
dz
d (f (z))
dz
d (g(z))
dz
d { f(z) . g(z) }
dz
d (g(z))
dz
d (f (z))
dz
d
dz
f (z)
g (z)
g (z) . – f (z) .
{g (z)}2
d f (z)
dz
d g(z)
dz
d
dz
d (f (z))
dz
(2z + 5)8
(1- 2z + z2)10
1+ i
? 2
f ?(z)
f ?(z)56
( Derivative )
z w = f(z) ?
z? z?
z? z?
z0 ( Differentiable ) f
z0 f
z0 f z0 f
Ex : let f(z) = ?z?2 is cont. fun. But isn t Diff.
( differentiation Formulas )
z
g (z) f (z) n k
z
?
?
? z z
f z f z f z
z z ?
?
? ?
?
( ) lim ( ) ( )
z
f z f z z f z
z ?
? ? ?
? ?
? ?
( ) ( )
( ) 0
0 lim ?
57
1) = 0
2) = 1
3) = k
4) = ±
5) = f (z) { } + { . g (z) }
6) { } =
7) { f(z)}n = n { f(z)}n-1 .
1
f (z) = z6 + 2z3 - 3
f (z) =
2
f (z) = 3z2 – z-1 , z0 = i
f (z) = z2 + 1 , z0 =
d (k)
dz
d (z)
dz
d ( k f(z) )
dz
d (f (z))
dz
d { f(z) ± g(z) }
dz
d (f (z))
dz
d (g(z))
dz
d { f(z) . g(z) }
dz
d (g(z))
dz
d (f (z))
dz
d
dz
f (z)
g (z)
g (z) . – f (z) .
{g (z)}2
d f (z)
dz
d g(z)
dz
d
dz
d (f (z))
dz
(2z + 5)8
(1- 2z + z2)10
1+ i
? 2
f ?(z)
f ?(z)