Derivatives · Tue, Nov 3, 2026

Answer: $\frac{4(4x + 2) - 4(4x + 4)}{(4x + 2)^{2}}$

1. Use the quotient rule.

   $$\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$$

2. Pick the top and bottom and differentiate each.

   $$u = 4x + 4,\quad v = 4x + 2,\quad u' = 4,\quad v' = 4$$

3. Substitute.

   $$\frac{4 \cdot (4x + 2) - (4x + 4) \cdot 4}{(4x + 2)^{2}}$$

4. So the answer is

   $$\frac{d}{dx}\left(\frac{4x + 4}{4x + 2}\right) = \frac{4(4x + 2) - 4(4x + 4)}{(4x + 2)^{2}}$$