Chain Rule. Let M, N and Q be differentiable manifolds, and let φ : M ?> N and N ?> Q be differentiable mappings. Prove that
or simply written
[Comment: To familiarize yourself with notations in Differential Geometry try to check the form that the above equality takes when you express the (differentials of the) maps and in terms of the (Jacobian) matrices obtained by choosing coordinate systems.]
The chain rule and differentiable mappings are investigated. The solution is detailed and well presented.