Calculus 3.1

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3.1 Derivatives
Great Sand Dunes National Monument, Colorado
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is called the derivative of at .
The derivative of f with respect to x is
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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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Note
dx does not mean d times x !
dy does not mean d times y !
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Note
(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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Note
(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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A function is differentiable if it has a
derivative everywhere in its domain. It must be
continuous and smooth. Functions on closed
intervals must have one-sided derivatives defined
at the end points.
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