Example 6: Power Rule

Find dy where

This problem can be worked by means of a double substitution. Let

u = x² + x, v = 1/u + 1.

Then 

y = v².

We find dy, dv, and du,

dy = 2v dv,
dv = -u^-2 du,
du = (2x + 1) dx.

Substituting, we get dy in terms of x and dx,