1. The problem is to find the derivative of the composite function $f(x) = (u \circ s)(x) = u(s(x))$ where $$u(x) = x^2 + x^4$$ $$s(x) = 3x + 2$$ 2. The formula for the derivative of a composite function (chain rule) is: $$D((u \circ s)(x)) = D(u(s(x))) = u'(s(x)) \cdot s'(x)$$ 3. First, find the derivatives of $u(x)$ and $s(x)$: $$u'(x) = \frac{d}{dx}(x^2 + x^4) = 2x + 4x^3$$ $$s'(x) = \frac{d}{dx}(3x + 2) = 3$$ 4. Substitute $s(x)$ into $u'(x)$: $$u'(s(x)) = 2(3x + 2) + 4(3x + 2)^3$$ 5. Now apply the chain rule: $$D((u \circ s)(x)) = u'(s(x)) \cdot s'(x) = \left[2(3x + 2) + 4(3x + 2)^3\right] \cdot 3$$ 6. Simplify the expression: $$= 3 \cdot 2(3x + 2) + 3 \cdot 4(3x + 2)^3 = 6(3x + 2) + 12(3x + 2)^3$$ 7. This is the derivative of the composite function $f(x)$. Final answer: $$f'(x) = 6(3x + 2) + 12(3x + 2)^3$$