## Mathematical Analysis## Differential Calculus |

## Are there higher derivatives of a function? |

Yes, there are higher derivatives of a function, often referred to as higher order derivatives. The “initial” derivative is often written as *f*' (*x*), but the “ ' ” is assumed in most cases. The next derivative is the second derivative (second order derivative), most often written as *f*'' (*x*); the next is the third derivative, or third order derivative, most often written as *f*''' (*x*); fourth derivative, or fourth order derivative, most often written as *f ^{(4)}(x);* and so on. The notation for the higher derivatives, or the

*n*th derivative, is as follows:

This equation is also seen written as *D ^{n} (y) = d^{n}y/dx^{n}.*