AP Calculus AB and BC glossary

Prime notation

Also called: Lagrange notation

Prime notation writes the derivative of f as f prime of x, the second derivative as f double prime, and so on. It is compact and reads well for named functions, but unlike Leibniz notation it does not state which variable you differentiated with respect to.

f'(x), \quad f''(x), \quad f'''(x), \quad f^{(4)}(x)

Past the third derivative the primes become unreadable, so a bracketed superscript takes over. That is why the fourth derivative is written with a parenthesised four rather than four tick marks.

The mistake

Using it for related rates. When several quantities all vary with time, prime notation hides which variable is which, and Leibniz form makes the chain rule visible instead.

Appears in: Unit 2: Defining the Derivative