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In Schwartz, Analysis, vol.I, is the following formula for scalar functions: $$ (f\circ g)^{(n)}(x)=\sum_{k_1+k_2+...+k_m=m} \frac{m!}{k_1! k_2! \ldots k_m! (1!)^{k_1} (2!)^{k_2} \ldots (m!)^{k_m} } $$ $$ g^{(k_1+k_2+\ldots +k_m)}(f(a)) (f')^{k_1}(a) (f'')^{k_2}(a) \ldots (f^{(m)})^{k_m}(a). $$ (the same is in Wikipedia) Is this formula true if $f,g$ are as in my question?
