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Differentiable functions.
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Differentiable functions.
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Differentiability at one point.
Definition
6
.
1
.
1
Let
be a function defined on a neighborhood of
. The function
is
differentiable
at
if the quotient
has a finite limit for
arbitrary close to
. This limit is called
the first derivative of
at
and is denoted by
.
Example
6
.
1
.
2
Let
and
. Then we have:
Thus:
We proved that
is differentiable at 1 and that
.
Example
6
.
1
.
3
Let
and
. Then we have:
Thus
We proved that
is differentiable at 2 and that
.
Definition
6
.
1
.
4
Sometimes, we denote:
Next:
The linear approximation of
Up:
Differentiable functions.
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Differentiable functions.
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Noah Dana-Picard 2007-12-28