Calculus 3.3

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2.3 Differentiation Rules
Larson, Hostetler, Edwards
Colorado National Monument
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• Review Old Topics to Build On
• Derivative of a Constant Rule
• Power Rule
• 2 Short-cut Rules (Simple Square Root and
  Reciprocal )
• Constant Multiplier Rule

• New Topics
• Product Rule
• Quotient Rule
• Higher Order Derivatives

Read pages 116 - 1126
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Review
If the derivative of a function is its slope,
then for a constant function, the derivative must
be zero.
example
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Review
This is part of a pattern.
examples
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Review
There are two simple shortcuts that evolve from
the Power Rule, the first is the
example
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Review
The second of the two simple shortcuts that
evolve from the Power Rule is the Simple
Reciprocal Rule.
example
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Review
constant multiple rule
examples
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sum and difference rules
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product rule
Notice that this is not just the product of two
derivatives.
This is sometimes memorized as
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Example
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quotient rule
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Applications of Derivatives
Find the horizontal tangents of
Plugging the x values into the original equation,
we get
(The function is even, so we only get two
horizontal tangents.)
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Higher Order Derivatives
(y double prime)
We will learn later what these higher order
derivatives are used for.
p
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Assignment page 124 - 125 Part - 1 Do 1 35
odds, 38, 40, 47 Part 2 Do 2 36 evens, 37,
39, 42