Derivative Operator

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 .

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

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.

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