1. The problem asks to find the derivative of the function $f(x) = (x^2 + 1)^2$ and then evaluate it at $x=2$. 2. We use the chain rule for differentiation: if $f(x) = [g(x)]^n$, then $f'(x) = n[g(x)]^{n-1} \cdot g'(x)$. 3. Here, $g(x) = x^2 + 1$ and $n=2$, so $$f'(x) = 2(x^2 + 1)^{2-1} \cdot \frac{d}{dx}(x^2 + 1) = 2(x^2 + 1) \cdot 2x = 4x(x^2 + 1).$$ 4. Now evaluate at $x=2$: $$f'(2) = 4 \cdot 2 \cdot (2^2 + 1) = 8 \cdot (4 + 1) = 8 \cdot 5 = 40.$$