If I have an equation given by

$$\displaystyle Y = \frac{a^2}{d^2}\frac{(1-c^2\frac{c}{a})}{(1-b^2)}$$

and I expand $a,b,c,d$ in a Taylor series, where $a$ is truncated at the $A^{th}$ order, $b$ is truncated at the $B^{th}$ order, $c$ is truncated at the $C^{th}$ order, and $d$ is truncated at the $D^{th}$ order, how do I go about determining the order of the truncation error for the full equation $ Y$?