Second and Higher Order Derivatives

Since the derivative $f'(x)$ of a function $y = f(x)$ is itself a function of $x$, it can, in turn, be differentiated. Differentiating $f'(x)$ once more with respect to $x$ gives the second-order derivative, written $\dfrac{d^2y}{dx^2}$ or $f''(x)$; differentiating again gives the third-order derivative, $\dfrac{d^3y}{dx^3}$ or $f'''(x)$; and so on.