Hey guys, so this may be a really silly question, but I'm trying to grasp a subtle point about higher-order derivatives of multivariable functions. In particular, suppose we have an infinitely differentiable function(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f: \mathbb{R}^{n} \rightarrow \mathbb{R}[/tex]

I know that the first derivative of this function is a linear map [tex]\lambda: \mathbb{R}^{n}\rightarrow\mathbb{R}[/tex]. However, when we take the second-derivative of [tex]\lambda[/tex], some questions arise for me:

1.) If we are taking this derivative when considering [tex]\lambda[/tex] as a linear function, then we'd just get back [tex]\lambda[/tex], which isn't the case. So how are we interpreting the first derivative when taking a second?

2.) In general, why do we say that [tex]D^{k}f:\mathbb{R}^{n^{k}}\rightarrow\mathbb{R}[/tex] and not [tex]D^{k}f:\mathbb{R}^{n}\rightarrow\mathbb{R}[/tex] ??

Thanks in advance.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Understanding of Higher-Order Derivatives

Loading...

Similar Threads - Understanding Higher Order | Date |
---|---|

B Need some help with understanding linear approximations | Feb 17, 2018 |

I Understanding an integral | Jan 31, 2018 |

I Euler Lagrange formula with higher derivatives | Jan 24, 2018 |

I Help with understanding inexact differential | Nov 13, 2017 |

I Rigorously understanding chain rule for sum of functions | Aug 6, 2017 |

**Physics Forums - The Fusion of Science and Community**