Third Derivative

Question 1

How to calculate a third derivative?

Answer

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

Question 2

What can be a third derivative for?

Answer

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.

Question 3

How to write a third derivative?

Answer

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.

Question 4

Which functions do not have a third order derivative?

Answer

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.

Third Derivative