Elements of the cotangent space can be thought of as infinitesimal displacements: if "f" is a differentiable function we can define at each point "p" a cotangent vector "dfp", which sends a tangent vector "Xp" to the derivative of "f" associated with "Xp". However, not every covector field can be expressed this way. Those that can are referred to as exact differentials. For a given set of local coordinates "xk," the differentials "dx" form a basis of the cotangent space at "p".