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 $\dot{y}$.