1. **State the problem:** Find the derivative of the function $$g(t) = \frac{1}{(8t + 1)^5}$$. 2. **Rewrite the function:** We can write $$g(t)$$ as $$g(t) = (8t + 1)^{-5}$$ to make differentiation easier. 3. **Use the chain rule:** The derivative of $$f(u) = u^n$$ is $$f'(u) = n u^{n-1}$$, and by the chain rule, $$\frac{d}{dt} f(g(t)) = f'(g(t)) \cdot g'(t)$$. 4. **Apply the chain rule:** $$ g'(t) = -5 (8t + 1)^{-6} \cdot \frac{d}{dt}(8t + 1) $$ 5. **Calculate the inner derivative:** $$ \frac{d}{dt}(8t + 1) = 8 $$ 6. **Combine results:** $$ g'(t) = -5 (8t + 1)^{-6} \cdot 8 = -40 (8t + 1)^{-6} $$ 7. **Rewrite the derivative in fraction form:** $$ g'(t) = -\frac{40}{(8t + 1)^6} $$ **Final answer:** $$ g'(t) = -\frac{40}{(8t + 1)^6} $$