Calculus 3.1

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3.1 Derivatives
Great Sand Dunes National Monument, Colorado
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the derivative of f with respect to x
f prime x
or
y prime
the derivative of y with respect to x
or
dee why dee ecks
the derivative of f with respect to x
or
dee eff dee ecks
the derivative of f of x
dee dee ecks uv eff uv ecks
or
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dx does not mean d times x !
dy does not mean d times y !
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(except when it is convenient to think of it as
division.)
(except when it is convenient to think of it as
division.)
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(except when it is convenient to treat it that
way.)
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In the future, all will become clear.
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(No Transcript)
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3.3 Differentiation Rules
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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examples
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constant multiple rule
examples
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constant multiple rule
sum and difference rules
(Each term is treated separately)
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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.
p
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Derivatives of trig functions
p