Tuesday, September 27
−
Lecture 8 :
Differentiation: Rules
(Refers to section 3.5 in
your text)
Students who have mastered the content of this lecture know about
:
The differentiation formulas: derivatives of sums, products, scalar products, quotients and the power rule.
Students who have practiced the techniques presented in this lecture will be able to
:
Find the
derivative of simple functions using the above differentiation formulas.
The following five differentiation formulas are important. The proof of the first four
follows directly from the definition of the derivative.
8.1
Theorem – Differentiation formulas for simple functions:
a)
For any constant
c
, the derivative of
f
(
x
)
=
c
is
b)
For the function
f
(
x
)
=
x
c)
Scaling rule
: If
c
is a constant and
f
(
x
)
is any function,
d)
Sum rule
: If
f
(
x
)
and
g
(
x
) are both differentiable on an interval (
a
,
b
) then is any
function,
e)
Power rule
: If
n
is a nonzero number and
f
(
x
) =
x
n
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View Full DocumentProof:
a)
b)
c)
d)
e) We will provide an easy proof of the
power rule
once we have learned logarithmic
differentiation.
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 Spring '11
 RobertAndre
 Calculus, Derivative, Scalar, Formulas

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