AP Calculus AB and BC glossary

Leibniz notation

Also called: dy/dx

Leibniz notation writes a derivative as dy over dx, which names both the changing quantity and the variable it changes with respect to. That explicitness makes it the standard notation for related rates, implicit differentiation, and any problem with several variables.

\frac{dy}{dx}

Prime notation is more compact and reads well for a single named function, as in $f'(x)$ . Leibniz notation carries more information and is what you want the moment more than one variable is in play.

The convention on this site follows the exam: primes for named functions, Leibniz for implicit differentiation and related rates, and never both inside one worked example.

Not a fraction

Treating $\frac{dy}{dx}$ as a genuine quotient is informal shorthand. It behaves like one in separable differential equations and substitution, but the symbol is defined as a limit.

Appears in: Unit 2: Defining the Derivative, Unit 3: Chain Rule, Implicit, and Inverses, Unit 4: Contextual Applications