Let S be a nonempty subset of a real normed space (X, ) and for some n ∈ N let ϕ1,...,ϕn : S → R be given functionals being continuous and directionally differentiable at an arbitrary x¯ ∈ S. Show...

Let S be a nonempty subset of a real normed space (X, ) and for some

n ∈ N let ϕ1,...,ϕn : S → R be given functionals being continuous and

directionally differentiable at an arbitrary x¯ ∈ S. Show that the directional

derivative of the functional f : S → R with