Suppose the units of
f
(
x
)
\displaystyle {f{{\left({x}\right)}}}
f
(
x
)
are liters, when
x
\displaystyle {x}
x
is measured in hours.
The units of
f
′
(
x
)
\displaystyle {f}'{\left({x}\right)}
f
′
(
x
)
will be
liter-hour
liters
liters/hour
\displaystyle \text{liters/hour}
liters/hour
liters/hour
2
\displaystyle \text{liters/hour}^{{2}}
liters/hour
2
And the units of
∫
f
(
x
)
d
x
\displaystyle \int{f{{\left({x}\right)}}}\ {\left.{d}{x}\right.}
∫
f
(
x
)
d
x
will be
liter-hour
liters
liters/hour
\displaystyle \text{liters/hour}
liters/hour
liters/hour
2
\displaystyle \text{liters/hour}^{{2}}
liters/hour
2
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