What's the partial derivative of $\partial _j h(a)=\partial_j(a)$?

Question

Let $h : \mathbb{R}^n\to \mathbb{R}^n, h(a)=a$. What's $\partial _j h(a)$?

$\partial_jh(a)=\partial_j(a)=\partial_j(a_1,...,a_j,...,a_n)=(0,...,1,...,0)$

is there a better way to notate this case?

Answer 1

Since $h_k=a_k$, $\partial_jh_k=\delta_{jk}$ so $\partial_jh=e_j$. Alternatively, $\nabla h=I_n$.