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With Planck cosmic microwave background observations, we established the spectral amplitude and tilt of the primordial power spectrum. Evidence of a red spectral tilt ($n_\mathrm{s}=0.96$) at $8σ$ provides strong support for the inflationary mechanism, especially the slow-roll of the effective scalar field in its nearly flat potential as the generator of scalar primordial perturbations. With the next generation of large-scale structure surveys, we expect to probe primordial physics beyond the overall shape and amplitude of the main, smooth and slowly-changing part of the inflaton potential. Using the specifications for the upcoming Euclid survey, we investigate to what extent we can constrain the inflation potential beyond its established slow-roll behaviour. We provide robust forecasts with Euclid and Planck mock data from nine fiducial power spectra that contain suppression and wiggles at different cosmological scales, using the Wiggly Whipped Inflation (WWI) framework to generate these features in the primordial spectrum. We include both Euclid cosmic shear and galaxy clustering, with a conservative cut-off for non-linear scales. Using Markov chain Monte Carlo simulations, we obtain an improvement in constraints in the WWI potential, as well an improvement for the background cosmology parameters. We find that apart from improving the constraints on the overall scale of the inflationary potential by 40-50 per cent, we can also identify oscillations in the primordial spectrum that are present within intermediate to small scales ($k\sim0.01-0.2\,\mathrm{Mpc^{-1}}$).