Leibniz's Notation For Differentiation
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, we can write:
Using Newton's notation, we can write:
For higher derivatives, we express them as follows:
denotes the nth derivative of ƒ(x) or y respectively. Historically, this came from the fact that, for example, the third derivative is:
which we can loosely write as:
Now drop the parentheses and we have:
The chain rule and integration by substitution rules are especially easy to express here, because the "d" terms cancel:
etc., and:
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