Calculus 3'3

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3.3 Rules for Differentiation
Colorado National Monument
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If the derivative of a function is its slope,
then for a constant function, the derivative must
be zero.
example
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If we find derivatives with the difference
quotient
We observe a pattern

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examples
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constant multiple rule
examples
When we used the difference quotient, we observed
that since the limit had no effect on a constant
coefficient, that the constant could be factored
to the outside.
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constant multiple rule
sum and difference rules
(Each term is treated separately)
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Example
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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product rule
Notice that this is not just the product of two
derivatives.
This is sometimes memorized as
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quotient rule
or
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Higher Order Derivatives
(y double prime)
We will learn later what these higher order
derivatives are used for.
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