1. **State the problem:** Find the derivative of the function $$f(x) = (x^2 + 1) \cdot \sin(x)$$ using the product rule. 2. **Recall the product rule formula:** If $$f(x) = u(x) \cdot v(x)$$, then the derivative is $$f'(x) = u'(x) \cdot v(x) + u(x) \cdot v'(x)$$. 3. **Identify the parts:** Here, $$u(x) = x^2 + 1$$ and $$v(x) = \sin(x)$$. 4. **Find the derivatives:** - $$u'(x) = \frac{d}{dx}(x^2 + 1) = 2x$$ - $$v'(x) = \frac{d}{dx}(\sin(x)) = \cos(x)$$ 5. **Apply the product rule:** $$f'(x) = u'(x) \cdot v(x) + u(x) \cdot v'(x) = 2x \cdot \sin(x) + (x^2 + 1) \cdot \cos(x)$$ 6. **Final answer:** $$\boxed{f'(x) = 2x \sin(x) + (x^2 + 1) \cos(x)}$$