# Derivative notation review

Review the different common ways of writing derivatives.

**Lagrange's notation:**

**Leibniz's notation:**

**Newton's notation:**$\dot y$

## What is derivative notation?

Derivatives are the result of performing a differentiation process upon a function or an expression. Derivative notation is the way we express derivatives mathematically. This is in contrast to natural language where we can simply say "the derivative of...".

## Lagrange's notation

In Lagrange's notation, the derivative of is expressed as (pronounced

*"f prime"*).This notation is probably the most common when dealing with functions with a single variable.

If, instead of a function, we have an equation like , we can also write to represent the derivative. This, however, is less common to do.

## Leibniz's notation

In Leibniz's notation, the derivative of is expressed as . When we have an equation we can express the derivative as .

Here, serves as an operator that indicates a differentiation with respect to . This notation also allows us to directly express the derivative of an expression without using a function or a dependent variable. For example, the derivative of can be expressed as .

This notation, while less comfortable than Lagrange's notation, becomes very useful when dealing with integral calculus, differential equations, and multivariable calculus.

## Newton's notation

In Newton's notation, the derivative of is expressed as $\dot f$ and the derivative of is expressed as $\dot y$.

This notation is mostly common in Physics and other sciences where calculus is applied in a real-world context.