If f1: M →M^' and f2: M^' →M^'' are mappings of class C^' between differentiable manifolds, show

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Step 1: Understand the composition of functions.u000AGiven two functions u005C( f_1: M u005Crightarrow Mu0027 u005C)

If $f_1: \mathrm{M} \rightarrow M^{\prime}$ and $f_2: \mathrm{M}^{\prime} \rightarrow M^{\prime \prime}$ are mappings of class $C^{\prime}$ between differentiable manifolds, show that $f_2 \circ f_1$ is a mapping of class $C^l$ and $$ d\left(f_2 \circ f_1\right)=d f_2 \circ d f_1 . $$