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We develop differential calculus of $C^{r,s}$-mappings on products of locallyconvex spaces and prove exponential laws for such mappings. As an application,we consider differential equations in Banach spaces depending on a parameter ina locally convex space. Under suitable assumptions, the associated flows aremappings of class $C^{r,s}$.

Differentiable mappings on products with different degrees of differentiability in the two factors