The Product Rule
The derivative of a product is not the product of derivatives.
Concept
First times d-second, plus second times d-first
When two functions multiply, each one contributes a change while the other holds still, so both terms appear in the answer.
Say it as a chant — 'first d-second plus second d-first' — and it becomes automatic.
(uv)′ = u·v′ + v·u′