Third derivative

In calculus, a branch of mathematics, the third derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing, used to define aberrancy. The third derivative of a function y=f(x) can be denoted by

Other notations can be used, but the above are the most common.

Let ${\displaystyle f(x)=x^{4}}$. Then ${\displaystyle f'(x)=4x^{3}}$, and ${\displaystyle f''(x)=12x^{2}}$. Therefore, the third derivative of f(x) is, in this case,

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