Leibniz's notation represents the derivative as an operation that can be taken on a function. Leibniz's notation can be written in many ways for the same function for example given the function the derivative can take the following forms.

The in the notation describes a small change in the thing it's being applied to (ie. describes an infinitely small change in ).

This small change in a variable or function is then used in the formal definition of average rate of change to give us the final notation we see above.

Higher Order Derivatives

Leibniz's notation for higher order derivatives can take the following forms

for the derivative. For example the first 3 derivatives of the variable can be expressed as follows

• First Derivative -
• Second Derivative -
• Third Derivative -