Taylor series.

can I write ?

i) $\displaystyle T^n_a(f+g) = T^n_a(f) + T^n_a(g) ; $

ii) $\displaystyle T^n_a(f*g) = T^n_a[T^n_a(f) * T^n_a(g)] ; $

iii) $\displaystyle T^n_a(f \circ g) = T^n_a[T^n_{g(a)}(f) \circ T^n_a (g)]; $

can I also this ?

iii) $\displaystyle T^n_a(f(g)) = T^n_a[T^n_{g(a)}(f(T^n_a(g)))] ; $


where I can find a guide of this taylor property in pdf?

Thanks to All !