Leibniz's notation for differentiation
See
Leibniz notation and
separation of variables for, among other things, an account of certain advantages of this notation over others.
In Leibniz's notation for differentiation, the derivative of the function f(x) is written:
If we have a
variable representing a function, for example if we set:
then we can write the derivative as:
Using
Lagrange's notation for differentiation, we can write:
Using the
Newton's notation for differentiation, we can write:
For higher derivatives, we express them as follows:
- or
denotes the nth derivative of f(x) or y respectively. Historically, this came from the fact that, for example, the 3rd derivative is:
which we can loosely write as:
Now drop the brackets and we have:
The
chain rule and
integration by substitution rules are especially easy to express here, because the "d" terms appear to cancel:
- etc.
and: