Prove that if f : U ⊂ ℝn → ℝn is differentiate at a ∈ ℝn, then the derivative is unique, t...

Prove that if f : U ⊂ ℝn → ℝn is differentiate at a ∈ ℝn, then the derivative is unique, that is, that there is only one linear transformation T such that

[Suggestion: Suppose, for a contradiction, that S and T are both derivatives of f at a and they differ at y. Then, on the one hand,

but on the other,