In n dimensions, the first derivative is an n-element vector. The second derivative is an n x n (symmetric) matrix. As n grows, the computation required to es

In n dimensions, the first derivative is an n-element vector. The second derivative is an n x n (symmetric) matrix. As n grows, the computation required to estimate the matrix increases (as at least n^2) and computation needed to use it increases (possibly faster). In practice, clever optimisation algorithms that use the 2nd derivative won't actually form this matrix.