Derivative Notation

We will now look at some types of notation for derivatives. The notation that is most commonly used on Math Online is Leibniz's and Lagrange's.

## Leibniz's Notation

In Leibniz's Notation, we write the derivative of a function $f$ with respect to $x$ as follows:

(1)
\begin{align} \frac{d}{dx} f(x) = \frac{df(x)}{dx} \end{align}
 Note: Leibniz notation is NOT division, so we don't read $\frac{d}{dx} f(x)$ as "$d$ divided by $dx$, $f(x)$." The notation $\frac{d}{dx}$ is known as an operator that operates on a function $f$.

## Lagrange's Notation

In Lagrange's Notation, we denote a derivative with a prime symbol "$'$" like $f'(x)$ or $y'$. This notation is common when Leibniz's notation could arise in messy equations.

## Euler's Notation

In Euler's Notation, we denote a derivative with a capital $D$, that is $D f(x)$ or $D y$. This notation has it's own limitations though as it doesn't tell us what variable to differentiate with respect to and is only used when understood clearly.

## Newton's Notation

Often in physics you will see Newton's notation of a derivative which uses a dot such as $\dot{y}$.