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Week One DQ’s
Day 2 Explain three rules for exponents listed in the chart on p. 239 (section 4.2). Do not
explain the first two definitions listed in the table (Exponent of 1 or 0). Create an
expression for your classmates to solve that uses scientific notation and at least one of the
rules for exponents you have described.
A negative exponent just means that the base is on the wrong side of the fraction line, so
you need to flip the base to the other side. For example, "
x
–2
" just means "
x
2
, but
underneath, as in 1/(
x
2
)".
The derivative of a product is the first factor times the derivative of the second plus the
second factor times the derivative of the first. For example, {
f
(x)
g
(x)}
'
=
f
(x)
g
'
(x)
+
f
'
(x)
g
(x).
The quotient rule says that the
derivative
of the
quotient
of two differentiable
functions
and
exists at all values of
as long as
and is given by the
formula
This is called the power rule. For example,
d
d
x
x
5
= 5x
4
It is usual to prove the power rule by means of the binomial theorem.
When a product is raised to a power, we can distribute that power through to each term
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 Spring '10
 ELLIOT

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