For a curve with radius vector , the unit tangent vector is defined by

(1)

(2)

(3)

where
is a parameterization variable, is the arc length, and an overdot
denotes a derivative with respect to , .
For a function given parametrically by , the tangent vector relative to the point is therefore given by

(4)

(5)

To actually place the vector tangent to the curve, it must be displaced by . It is also true that