Chapter 13.4, Problem 59ES

Suppose that certain measured quantities x and y have errors of at most $r\%\text{ and }s\%,$ respectively. For each of the following formulas in x and y, use differentials to approximate the maximum possible error in the calculated result.

$\begin{array}{|l|}\hline \left(\text{a}\right)xy\hfill \\ \left(\text{b}\right)x/y\hfill \\ \left(\text{c}\right)x^2{y}^3\hfill \\ \left(\text{d}\right)x^3\sqrt{y}\hfill \\ \hline\end{array}$