Title might not be approriate but I am not sure how to ask this. I have a question asking to find the error rate and in one of the steps, the fraction flips. I suspect it's because we are trying to make denominators the same, but I really have no clue.
Question: We want to estimate the relative error $dg/g$ using the relative error for time $dt/t$.
This is the supplied information;
$g = \frac{10}{t^2}$
and
$\frac{dg}{dt}=-\frac{20}{t^3}$
The provided equation is: $\frac{dg}{g}=\frac{1}{g}\cdot \frac{dg}{dt}\cdot dt$
The next step is: $\frac{t^2}{10}\cdot \left(-\frac{20}{t^3}\right)\cdot dt$
So how or why did g ($\frac{10}{t^2}$) change to $\frac{t^2}{10}$?