## Mathematical Analysis## Differential Calculus |

## What is an example of the second derivative? |

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 *d ^{2}y/dx^{2}*, 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.