Managed DirectX is a new technology introduced by Microsoft. It is a set of libraries - or as referred to in .NET _assemblies_ - to create applications that utilise DirectX. Each of the DLL's is used with a specific sub-system. The DLL's are as below.
Microsoft.DirectX (Microsoft.DirectX Namespace): Very simple assembly. It contains vector and matrix classes which are very extensive. The matrix class speeds up tasks like translation by providing static and intance functions to translate a matrix.
Microsoft.DirectX.Direct3D (Microsoft.DirectX.Direct3D Namespace): This is the base assembly, and is generally the most used one.
Microsoft.DirectX.Direct3DX (Microsoft.DirectX.Direct3D Namespace): A very useful extensive of the Direct3D namespace. It contains helper classes including the Mesh + MeshLoader classes, the Effect class for manipulating the HLSL, helper classes for rendering to surfaces, and a whole lot more. Anyone wishing to develop a game (no matter how simple) will probably need this class for using meshs.