In the book of Frankel, The Geometry of Physics, at page 45, he states that
A Riemannian metric on a manifold $M^n$ assigns, in a differentiable fashion, a positive definite inner product $⟨, ⟩$ in each tangent space $M_p^n$ .
However, what does he mean by "in a differentiable fashion" ? I know what is differentiable manifold, but I don't understand how can the assignment of a metric tensor be differentiable ?