AP Calculus AB and BC glossary
Sum and difference rule
The derivative of a sum is the sum of the derivatives, and the same holds for a difference. This is what makes differentiation term by term legal, and it is why a polynomial can be differentiated one piece at a time.
Differentiation is linear, which is the formal name for this rule combined with the constant multiple rule. Integration shares the property, which is why both operations distribute across sums.
The mistake
Extending it to products or quotients. There is no product rule of this shape: the derivative of a product is not the product of the derivatives.
Appears in: Unit 2: Defining the Derivative