The exterior derivative df of a function f is a covector field, i.e. an assignment of a cotangent vector to each point p, by definition such that d f ( X ) = X f , for each vector field X. A vector field is an assignment of a tangent vector to each point p. In coordinates X can be expanded at each point p in the basis given by the ∂/∂ x | p. Applying this with f = x, the coordinate function itself, and X = ∂/∂ x, called a coordinate vector field, one obtains d x μ μ ( ∂ ∂ ∂ ∂ x ν ν ) = ∂ ∂ x μ μ ∂ ∂ x ν ν = δ δ ν ν μ μ .