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\begin{document}$$\mathcal {A}$$\end{document} and U\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {U}$$\end{document} be Banach algebras such that U\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {U}$$\end{document} is also a Banach A\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A}$$\end{document}-bimodule with compatible algebra operations, module actions and compatible norm. By defining an appropriate multiplication, we turn ℓ1\documentclass[12pt]{minimal}
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\begin{document}$$\ell ^1$$\end{document}-direct product A×U\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A}\times \mathcal {U}$$\end{document} into a Banach algebra so that A\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A}$$\end{document} is a closed subalgebra and U\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {U}$$\end{document} is a closed ideal of it. This algebra is, in fact, the semidirect product of A\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A}$$\end{document} and U\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {U}$$\end{document} which we denote by A⋉U\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A} < imes \mathcal {U}$$\end{document}. In this paper, we study automatic continuity of derivations on A⋉U\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A} < imes \mathcal {U}$$\end{document} in a general setting. As an application of our results, we present various results about the automatic continuity of derivations of module extension Banach algebras and θ\documentclass[12pt]{minimal}
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\begin{document}$$\theta $$\end{document}-Lau products of Banach algebras. Some examples are also given.
