Taking the derivative of an expression denoted with the fraction where the denominator contains the variable you are taking the derivative with respect to. For example, the derivative notation typically appears in an expression like this:

In plain language, this means take the derivative of the function with respect to the variable . When referencing the derivative as a function itself the following notation is used:

When evaluating the derivative given a specific input, like the following notation is used:

Implicit in the notation of the derivative is the idea of limits. For example, the derivative notation can be expanded into the equivalent limit notation like so:

Another notation that is commonly used to denote a derivative is the apostrophe notation. Typically, this notation is used in an expression like this:

The preferred notation for this site is the notation.

An antiderivative of a function f(x) is represented by a function F(x) such that the derivative of F(x) is f(x). Essentially, an antiderivative reverses the process of differentiation.

The integral operator is written using the integral symbol ∫ and has four parts: the expression being integrated, the differential, and start value and an end value.