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Question

# State the unit associated with the following derivatives and state the physical meaning of each derivative. $f^{\prime}(t)$

Solution

Verified

$f(t)$ tells us the ratio of wing cord length to weight of an $t$ weeks old owlet.

Therefore, unit that describes the growth rate of the described ratio:

\begin{align*} f' (t) \hspace{0.2cm}&= \hspace{0.2cm}\left(\frac{w}{m}\right)^{'}\\ &=\hspace{0.2cm}\frac{w' m - wm'}{m^2}\\ &=\hspace{0.2cm}\frac{\text{grams}\cdot \text{millimeters weeks}^{-1}}{\text{grams}^2}\\ &=\hspace{0.2cm}\frac{\text{millimeters}}{\text{grams}\cdot\text{week}} \end{align*}

It tells us how many millimeters has cord grown per each gram that owlet has gained and each week that it is older.

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