AP Calculus AB and BC glossary
Constant multiple rule
Also called: Sum rule
The constant multiple rule says a constant factor passes straight through a derivative, and the sum rule says the derivative of a sum is the sum of the derivatives. Together they make differentiation linear.
Linearity is why long polynomials are differentiated term by term with no extra machinery. It also carries over to integration, where constants factor out and sums split apart in exactly the same way.
Sums only
Linearity applies to sums and constant multiples, never to products or quotients of two functions of the variable. Those need their own rules.
Appears in: Unit 2: Defining the Derivative