 For readability of the formulas, the arguments formula_26 are omitted.The curvature formula_35 at a regular point is given by the formula

The implicit function theorem guarantees within a neighborhood of a point formula_26 the existence of a function formula_38 such that formula_39.By the chain rule, the derivatives of function formula_38 are
(where the arguments formula_43 on the right side of the second formula are omitted for ease of reading).