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The third derivative (or 3rd order derivative/differentiation) is the application of the derivative on the second derivative of a function (which is itself the application of the derivative to the first derivative of the function).

In physics, the third derivative can be used to characterize the jerk, the variation of the acceleration, it is the derivative of the acceleration with respect to time. It can be studied to assess comfort in transport.

How to write a third derivative?

A third derivative can be written either $ f´´´(x) $, or $ f^{(3)}(x) $, or $ \frac{d^3f}{dx^3} $.

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Cite as source (bibliography): Third Derivative on dCode.fr [online website], retrieved on 2023-02-08, https://www.dcode.fr/third-derivative