Notation

The symbols for the successive derivatives are usually abbreviated as follows:

$$\begin{array}{rl} \frac{d}{dx} \left ( \frac{dy}{dx} \right ... ...^{n-1}y}{dx^{n-1}} \right ) & = \frac{d^ny}{dx^n}. \end{array}$$

If $y = f(x)$, the successive derivatives are also denoted by

$$f'(x),\ f''(x),\ f'''(x),\ f^{(4)}(x),\ ...,\ f^{(n)}(x);$$

or

$$y',\ y'',\ y''',\ y^{(4)},\ ...,\ y^{(n)};$$

or,

$$\frac{d}{dx} f(x),\ \frac{d^2}{dx^2} f(x), \ \frac{d^3}{dx^3} f(x),\ \frac{d^4}{dx^4} f(x), \ ...,\ \frac{d^n}{dx^n} f(x).$$