Expressed in terms of Leibniz's notation for differentiation we have:
etc.
Expressed in dot notation we have:
etc.
Sometimes Newton's notation is more useful than Leibniz's, for example when calculating the derivative at a point.
In Newton's notation, if you know f(x) and you want to calculate f '(x) at a point k, you would write:
and this represents that derivative. For example, if f(x) = x2, then f '(3) = 6. The same thing under Leibniz's notation is more cumbersome:
Leibniz's notation is versatile in that it allows you to specify the variable for differentiation (in the denominator). This is especially relevant for partial differentiation.
Newton did not develop a standard notation[?] for integration, he seemed to use lots of different notations. However the widely adopted notation[?] is Leibniz's notation for integration[?].
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