The second derivative is actually a function’s derivative’s derivative. In other words, the function’s derivative may also have its own derivative, called the second derivative or second order derivative. If we let y = f(x), the second derivative becomes d/dx(dy/dx). This is equal to d2y/dx2, further represented by the symbols f' (x) or y’ One good example of a second order derivative is acceleration—it is actually the second derivative of a change in distance. In other words, the first derivative gives instantaneous velocity (see above) while the second derivative gives acceleration.