Tangent spaces of differentiable manifolds are Euclidean vector spaces. Let formula 27 be any continuously differentiable bijection. Two important classes of differentiable manifolds are smooth and analytic manifolds. The inverse function theorem can be rephrased in terms of differentiable maps between differentiable manifolds. Differential topology is the field dealing with differentiable functions on differentiable manifolds. Furthermore, the interpolant is a polynomial and thus infinitely differentiable. It is possible to develop a calculus for differentiable manifolds. This is the standard way differentiable manifolds are defined. These definitions extend to differential maps between differentiable manifolds in the following way. Let formula 14 be a Riemannian manifold and let formula 67 be a differentiable map. They are also often monotonically increasing, continuous, differentiable and bounded. Harmonic functions are infinitely differentiable in open sets. Let be a proper parametric representation of a twice differentiable plane curve. Some also use differentiable or even analytic functions. The derivative of a real differentiable function is a real function.