Differentiation Notation

Named after Gottfried Leibniz, the Leibniz Notation is the most common and likely the one you are most familiar with.

It is most commonly used when the equation of is used and mapped to the axis. This is as there needs to be a dependent relationship between the variables and . Note: the variables and don't have to be used, they can be replaced with whatever variables you are using at the time.

Given the function, , the derivative would be written as:

If the derivative is taken again another prime mark is added:

When it becomes too cumbersome to add prime marks the marks are replaced with a number in parentheses:

With the number indicating the derivative order.

Also known as dot notation, newton's notation denotes derivatives by a dot over the dependent variable:

Multiple dots represent higher order derivatives:

One notices that the independent variable ( in this case) is not specified explicitly and must be inferred by context.

Given the function the first order derivative would be written as:

Higher order derivatives can be expressed using an exponent

See W2L4 - Higher Order Linear ODEs for details.