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The product rule states (uv)' = u'v + uv'. Both terms are needed because changing either factor changes the product, and the total rate is the sum of the two effects.
Product rule
(uv)' = u'v + uv'
2x·sin x + x²·cos x = 4 sin 2 + 4 cos 2 ≈ 3.6372624 − 1.6645873 ≈ 1.9726751.
No, and that is the most common mistake. Only the sum u'v + uv' is correct.