Chapter 4 – Differentiation
Section 4.1 – The Algebra of Derivatives
Pg 69, Definition – Let I be an open interval containing the point x
o
. Then the function is said to be
differentiable
at x
o
if
exists, in which case we denote this limit by
and call it the derivative of
at x
o
; that is
If the function is differentiable at every point in I, we say that
is differentiable and call the function
the
derivative
of .
Pg 71, Proposition 4.1 – For a natural number n, define
for all x in R. Then the function
is differentiable and
Pg 72, Proposition 4.2 – Let I be an open interval containing the point x
o
, and suppose that the function
is
differentiable at x
o
. Then
is continuous at x
o
.
Pg 72, Theorem 4.3 – Let I be an open interval containing the point x
o
, and suppose that the functions
and
and
differentiable at x
o
. Then
(i) is differentiable at x
o
and
(ii) is differentiable at x
o
and
(iii)if
for all x in I, then
is differentiable at x
o
and
Pg 74, Proposition 4.4 – For an integer n, define
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 Spring '11
 Higdon
 Calculus, Algebra, Derivative, Continuous function, open interval

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