Let
D
:
C
n
[
0
,
1
]
→
M
D:{C^n}\left [ {0,1} \right ] \to \mathcal {M}
be a derivation from the Banach algebra of
n
n
times continuously differentiable functions on
[
0
,
1
]
\left [ {0,1} \right ]
into a Banach
C
n
[
0
,
1
]
{C^n}\left [ {0,1} \right ]
-module
M
\mathcal {M}
. If
D
D
is continuous then it is completely determined by
D
(
z
)
D\left ( z \right )
where
z
(
t
)
=
t
,
0
≤
t
≤
1
z\left ( t \right ) = t,0 \leq t \leq 1
. For the case when
D
D
is discontinuous we show that
D
(
f
)
D\left ( f \right )
is determined by
D
(
z
)
D\left ( z \right )
for all
f
f
in an ideal
T
(
D
)
2
\mathcal {T}{\left ( D \right )^2}
of
C
n
[
0
,
1
]
{C^n}\left [ {0,1} \right ]
where its closure
T
(
D
)
2
¯
\overline {\mathcal {T}{{\left ( D \right )}^2}}
is of finite codimension.