Differentiation of a function \(f(x)\) yields the derivative \(f'(x)\), which is also written as \(\displaystyle\frac{\dd f}{\dd x}(x)\) and \(\displaystyle\frac{\dd}{\dd x}f(x)\tiny.\) This derivative is a function of \(x\) that we can differentiate again (at least for very smooth functions). This yields the second derivative of \(f(x)\). Common formats for this are \(\displaystyle f''(x), \frac{\dd^2f}{\dd x^2}\!(x)\) and \(\displaystyle\frac{\dd^2}{\dd x^2}\!f(x)\)
(Note the different placement of the number 2 above and below the 'division' line in the last two notations).

We have formed the derivative of a derivative formed and we can go. At \(n\) time differentiating feature \(f(x)\) we get the \(n\)-th derivative. In general, the \(n\)-th derivative with \(n>2\) is written in one of the following formats: \(\displaystyle f^{(n)}(x), \frac{\dd^nf}{\dd x^n}(x)\) and \(\displaystyle\frac{\dd^n}{\dd x^n}\!f(x)\).