# Math 22 Higher-Order Derivative

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## Higher-Order Derivatives

``` The "standard" derivative ${\displaystyle f'(x)}$ is called the first derivative of ${\displaystyle f(x)}$. The derivative of ${\displaystyle f'(x)}$ is the second derivative of${\displaystyle f(x)}$, denoted by ${\displaystyle f''(x).}$
By continuing this process, we obtain higher-order derivative of ${\displaystyle f(x)}$.
```

Note: The 3rd derivative of ${\displaystyle f(x)}$ is ${\displaystyle f'''(x)}$. However, we simply denote the ${\displaystyle n^{th}}$ derivative as ${\displaystyle f^{(n)}(x)}$ for ${\displaystyle n\geq 4}$

## Notes

If ${\displaystyle f(x)}$ is the position function, then ${\displaystyle f'(x)}$ is the velocity function and ${\displaystyle f''(x)}$ is the acceleration function.