Curvilinear Motion:

Let a particle moving along a plane curve AB as illustrated in Figure. At any point P on the curve, we may ascertain two directions, normal and tangential to the curve. Let t^ be the unit tangent vector and n^ be the unit normal vector at P. this is clear that the directions of the normal and tangent shall vary at various points.

At any other point P′, unit tangent vector t^′ and unit normal vector n^′ shall be in different directions from t^ and n^ at P. Therefore t^ and n^ are unit vectors of constant magnitudes but variable in directions. Therefore, they may be differentiated.