What is the simplest adequate model of shear thinning and extension thickening of polymer solutions at the intense local deformation rates in coating and related flows? We examine a combination of the Carreau equation of shear sensitivity with an analogous equation of extension sensitivity. The two contributions are mediated by the rate at which the principal straining axes turn with respect to the liquid itself, a relative rotation rate that is frame independent, vanishes in purely extensional flow, and harks back to Lumley’s (1969) idea of persistent molecular strain rate, which was adumbrated by Takserman‐Krozer (1963) and named by Frank and Mackley (1976). We indicate how the new equation can be used to extract viscosity‐in‐extension from the extension‐rich mixed flow between opposed nozzles. We illustrate how the new equation can be applied to the complex mixed flow in slide coating.