It is known that for $f:\mathbb{R} \rightarrow \mathbb{R}$,
$$f(a + h) = f(a) + f'(a)h + O(h^2)$$
Is there a similar expression for $f:\mathbb{R}^n \rightarrow \mathbb{R}$? i.e., something like
$$f(a+h) = f(a) + \nabla f(a) \cdot h + O(\|h\|^2)$$
Thanks.