I was reviewing basic calculus of of functions of several variables. It struck me that in one of the exercises, it was required to show that a given function has directional derivative for all directions at the origin (0,0) even though it is not continuous at (0,0).(adsbygoogle = window.adsbygoogle || []).push({});

Without getting into the details , I thought that this does not make sense as the function has to be differentiable at (0,0) for the directional derivatives to exist. And differentiability implies the continuity of the function at (0,0).

Am I missing something here?

**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!

# Directional Derivative of a discontinuous function

Loading...

Similar Threads - Directional Derivative discontinuous | Date |
---|---|

I Directional Derivative demonstration | Jan 1, 2018 |

I Directional derivative | Mar 7, 2017 |

I A directional, partial derivative of a scalar product? | Feb 5, 2017 |

I Directional derivative: identity | Nov 23, 2016 |

I Problem with directional derivative | Jul 1, 2016 |

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