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Third Derivative

Tool for Third Derivative calculation f''', so 3 times the application of the derivation to a function, a triple derivation on the same variable.

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Third Derivative -

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# Third Derivative

## Third Derivative Calculator

### How to calculate a third derivative?

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).

Example: $$f(x) = x^3+\sin(x) \\ \Rightarrow f´(x) = 3 x^2+\cos(x) \\ \Rightarrow f´´(x) = 6x - \sin(x) \\ \Rightarrow f´´´(x) = 6 - \cos(x)$$

### What can be a third derivative for?

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 $\frac{d^3f}{dx^3}$.

On dCode always use f ' ' ' especially for differential equations.

### Which functions do not have a third order derivative?

All the non-continuous and / or non-derivable functions (in at least one point of their domain of definition) have no derivative and therefore have no second derivative or third derivative.

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Third Derivative on dCode.fr [online website], retrieved on 2023-02-08, https://www.dcode.fr/third-derivative

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