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Derivatives of
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Second derivatives, third derivatives, etc.
This section, in which we differentiate again and again, couldn't be much simpler. We know how
to take the derivative of a function already, no problem, easy street. The result, written
f
'(
x
), is
itself a function of
x
. But then we can take its derivative again, writing it as
f
''(
x
), and calling it
the second derivative of
f
(
x
). It's like running meat through a grinder a second time before you
put the patties on the grill. Makes it so mushy and tender, just the way you like them. (For
vegetarians, change the analogy to smoothies in the blender.)
For example, if
f
(
x
) = 2
x
3
, then
f
'(
x
)= 6
x
2
and
f
''(
x
)=12
x
.
We'll talk about what second derivatives are good for when we discuss graphing .
Now, as Liz Taylor realized after her second marriage, ``Why stop at two?" We can keep
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 Derivatives, Derivative, JOEL HASS, Liz Taylor

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