Difference between revisions of "Order (derivative)"
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The function <math>f(x)</math> itself is the order-<math>0</math> derivative, the ordinary (first) derivative has order <math>1</math>, the second derivative has order <math>2</math>, and so on. In general, the derivative of order <math>k</math> is called the <math>k</math>th derivative. | The function <math>f(x)</math> itself is the order-<math>0</math> derivative, the ordinary (first) derivative has order <math>1</math>, the second derivative has order <math>2</math>, and so on. In general, the derivative of order <math>k</math> is called the <math>k</math>th derivative. | ||
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[[Category: Definition]] | [[Category: Definition]] | ||
Latest revision as of 16:40, 15 March 2022
The order of a derivative is the number of successive differentiations performed to obtain the derivative from the original function. Formally, using Lagrange's notation for the derivative, the order-
derivative is defined recursively by 
The function 
itself is the order-
derivative, the ordinary (first) derivative has order 
, the second derivative has order 
, and so on. In general, the derivative of order is called the th derivative.
