Past exam of the options II course of the University of Oxford / 2011 / F / F2 / a / ii / Solution

For a scalar-valued differentiable function, its gradient is the column vectorIt represents the total derivative by the Euclidean inner product: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.