When a function is a product uv, both factors can change, so the derivative accounts for each changing while the other is held: (uv)' = u'v + uv'. Differentiating each factor separately and combining avoids expanding first when that would be messier.

Steps

1. Identify u and v; compute u' and v'.
2. Form u'v + uv'.
3. Expand and combine like terms if helpful.