Derivatives · Thu, Nov 5, 2026

Answer: $\frac{8}{8x + 6}$

1. Use the chain rule: differentiate the outer function, leave the inside alone, then multiply by the derivative of the inside.

   $$\frac{d}{dx} f(u) = f'(u) \cdot u'$$

2. The inside function and its derivative are

   $$u = 8x + 6,\quad u' = 8$$

3. The derivative of the outside function, in terms of u, is

   $$\frac{d}{du}\ln u = \frac{1}{u}$$

4. So the answer is

   $$\frac{d}{dx}\left(\ln(8x + 6)\right) = \frac{8}{8x + 6}$$