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We adopt the viewpoint that topological And\'e-Quillen theory for commutative$S$-algebras should provide usable (co)homology theories for doing calculationsin the sense traditional within Algebraic Topology. Our main emphasis is onhomotopical properties of universal derivations, especially their behaviour inmultiplicative homology theories. There are algebraic derivation properties,but also deeper properties arising from the homotopical structure of the freealgebra functor $\mathbb{P}_R$ and its relationship with extended powers ofspectra. In the connective case in ordinary $\bmod{\,p}$ homology, this leadsto useful formulae involving Dyer-Lashof operations in the homology ofcommutative $S$-algebras. Although many of our results could no doubt beobtained using stabilisation, our approach seems more direct. We also discuss areduced free algebra functor $\tilde{\mathbb{P}}_R$.

Calculating with topological Andr\'e-Quillen theory, I: Homotopical properties of universal derivations and free commutative $S$-algebras