some code to support the realization I can obviate many steps

Author: pavelkomarov

notebooks/README.md

@@ -12,4 +12,5 @@
 | [DFT Play](https://github.com/pavelkomarov/spectral-derivatives/blob/main/notebooks/dft_play.ipynb) | Due to aliasing, it's possible to find the DFT coefficients with many different combinations of wavenumbers, so long as they cover $\{0, ...N\}$ modulo $N$. Here lies some code to demonstrate this fact.|
 | [Filtering Noise](https://github.com/pavelkomarov/spectral-derivatives/blob/main/notebooks/filtering_noise.ipynb) | |
 | [Fourier](https://github.com/pavelkomarov/spectral-derivatives/blob/main/notebooks/fourier.ipynb) | Usage examples of `fourier_deriv`, in one and multiple dimensions, with an emphasis of when this method will work and when it will break.|
-| [Fourier Periodic Extensions](https://github.com/pavelkomarov/spectral-derivatives/blob/main/notebooks/fourier_periodic_extensions.ipynb) | It's sometimes possible to take even and odd extensions of a function and produce something periodic or nearly periodic, which can then be spectrally differentiated with the Fourier basis. This notebook demonstrates how to do this.|
+| [Fourier Periodic Extensions](https://github.com/pavelkomarov/spectral-derivatives/blob/main/notebooks/fourier_periodic_extensions.ipynb) | It's sometimes possible to take even and odd extensions of a function and produce something periodic or nearly periodic, which can then be spectrally differentiated with the Fourier basis. This notebook demonstrates how to do this.|
+| [Stay in x Domain](https://github.com/pavelkomarov/spectral-derivatives/blob/main/notebooks/stay_in_x_domain.ipynb) | There is actually a simple derivative rule for a Chebyshev series, analogous to the rule for Power series, and we can exploit it to find spectral derivatives without some of the complicated steps. |