Sunspot drawings made by Galileo Galilei in 1612 are used to derive the law of differential rotation at that time. The main interest of the work is during the time of observations, just at the beginning of telescopic observations and some decades before the Maunder Minimum (1645 1715), a period where the sunspots almost disappeared from the solar surface. For this purpose we have carried out careful corrections of the different sources of errors derived from the observing technique. By comparing with other results of the same century, a significant difference is only detected by comparing with data corresponding to the deep Maunder Minimum (Paris Observatory drawings). The characteristics of the solar differential rotation, and extrapolating the behavior of solar activity, did not differ before or after the Maunder Minimum. We also include an analysis of hitherto ignored sunspot drawings by N. Bion made in October and November 1672.