If $y = \frac{(x + 1)^{2}}{(x + 3)^{4}}$ for $x > -1$, what is $\frac{1}{y}\frac{dy}{dx}$?

Explanation

1. 01

   Take logs: $\log y = 2\log(x + 1) - 4\log(x + 3)$.

2. 02

   Differentiate: $\frac{1}{y}\frac{dy}{dx} = \frac{2}{x + 1} - \frac{4}{x + 3}$.