 In what follows, the partial derivatives are denoted formula_18 (for the derivative with respect to "x"), formula_19, formula_20 (for the second partial with respect to "x"), formula_21 (for the mixed second partial), formula_22

A curve point formula_23 is "regular" if the first partial derivatives formula_24 and formula_25 are not both equal to 0.The equation of the tangent line at a regular point formula_26 is

so the slope of the tangent line, and hence the slope of the curve at that point, is

If formula_29 at formula_30 the curve is vertical at that point, while if both formula_31 and formula_32 at that point then the curve is not differentiable there, but instead is a singular point – either a cusp or a point where the curve intersects itself.A normal vector to the curve at the point is given by 
(here written as a row vector).