Hi, I have a small question about this. Using the chain rule, I know that a composition of differentiable functions is differentiable. But is it also true that if a composition of functions is differentiable, then all the functions in the composition must be differentiable?(adsbygoogle = window.adsbygoogle || []).push({});

For example, if [itex]f(g(x))[/itex] is differentiable, does that imply [itex]f(x)[/itex] and [itex]g(x)[/itex] are both differentiable?

Thanks!

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

Dismiss Notice

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!

# Differentiability of composite functions

Loading...

Similar Threads - Differentiability composite functions | Date |
---|---|

I Linearity of the Differential ... Junghenn Theorem 9.2.1 ... | Mar 1, 2018 |

I Differentiation on R^n ...need/ use of norms ... | Mar 1, 2018 |

I Multivariable Analysis ...the derivative & the differential | Feb 27, 2018 |

I Multivariable Differentiation - Component Functions ... | Feb 20, 2018 |

B Monotony of composite functions | Mar 12, 2016 |

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