Derivative Operator

Derivative Notation Annotated

The derivative is one of the main operators in calculus. The derivative of a function with a respect to returns a function that represents the change in over the change in . For example, the derivative operator typically appears in an expression like this:

In plain language, this means take the derivative of the function with respect to the variable .

Definition

The formal limit definition of the derivative operator is given below.

Common Derivatives

The table below shows some common derivatives for polynomial, trigonometric and exponential functions. The coefficients , and are highlighted blue to make them distinct from the variables of the functions.

Function Derivative
Constant
Line
Quadratic
Cubic
Polynomial
Sine
Cosine
Exponential
Logarithm

Rules

Shown below are some common rules when taking the derivatives of more complex functions.

Name Rule
Sum Rule
Product Rule
Power Rule
Chain Rule