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 nth derivative, is as follows:

This equation is also seen written as Dⁿ (y) = dⁿy/dxⁿ.