If the function f is differentiable on an interval, its derivative f′ is defined. If f′ is also differentiable, then the derivative of this, denoted by f″, is the second derivative function of f.

Similarly, if f″ is differentiable, then f‴(x) or d³f/dx³, the third derivative of f at x, can be formed, and so on. The nth derivative of f at x is denoted by f⁽ⁿ⁾(x) or dⁿf/dxⁿ. The nth derivatives, for n ≥ 2, are called the higher derivatives of f. When y = f(x), the higher derivatives may be denoted by d²y/dx²,…, dⁿy/dxⁿ or y″, y‴,…, y⁽ⁿ⁾.