Solution
= Solution
For a scalar-valued differentiable function, its <gradient> is the column vector
$$
\nabla f(x)=\begin{pmatrix}\partial_1f(x)\\\vdots\\\partial_nf(x)\end{pmatrix}.
$$
It represents the <total derivative> by the <Euclidean inner product>:
$$
\boxed{Df(x)h=\nabla f(x)\cdot h.}
$$
Thus $J_f(x)=\nabla f(x)^T$ is a row matrix; the <gradient> and the <total derivative> represent the same first-order information but have different types.