Can you help me with this? I know that in a 1-dimensional case, Taylor expansion of composite function is of the following type:
$$f(g(x))=f(g(a))+f'(g(a))g'(a)(x-a)$$
I need the formula for Taylor expansion for the following problem. Let function $f$ be scalar function, $\textbf{g}=(g_1,g_2)$ vector function, $\textbf{x}=(x_1,x_2,x_3,x_4)$ and $\textbf{a}=(a_1,a_2,a_3,a_4)$. My guess is: $$f(\textbf{g(x)})=f(\textbf{g(a)})+Df(\textbf{g(a)})D\textbf{g(a)}(\textbf{x-a})^T$$ Am I correct?