IMathAS-libretexts

Suppose the units of

\displaystyle {f{{\left({x}\right)}}}

are

\displaystyle \frac{\text{gallons}}{\text{day}}

, when

\displaystyle {x}

is measured in days.

The units of

\displaystyle {f}'{\left({x}\right)}

will be

gallons $\displaystyle \cdot$ days
gallons
$\displaystyle \text{gallons}^{{2}}$
$\displaystyle \frac{\text{gallons}}{\text{day}}$
$\displaystyle \frac{\text{gallons}}{\text{day}^{{2}}}$
$\displaystyle \frac{\text{gallons}^{{2}}}{\text{day}}$
$\displaystyle \frac{\text{gallons}^{{2}}}{\text{day}^{{2}}}$

And the units of

\displaystyle \int{f{{\left({x}\right)}}}\ {\left.{d}{x}\right.}

will be

gallons $\displaystyle \cdot$ days
gallons
$\displaystyle \text{gallons}^{{2}}$
$\displaystyle \frac{\text{gallons}}{\text{day}}$
$\displaystyle \frac{\text{gallons}}{\text{day}^{{2}}}$
$\displaystyle \frac{\text{gallons}^{{2}}}{\text{day}}$
$\displaystyle \frac{\text{gallons}^{{2}}}{\text{day}^{{2}}}$

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