ParametricDerivative Command

ParametricDerivative[<Curve x=x(t), y=y(t)>]

Returns a new parametric curve given by \left( x(t), \frac{y'(t)}{ x'(t)} \right) .

Example: ParametricDerivative[Curve[2t, t², t, 0, 10]] returns the parametric curve (x(t) = 2t, y(t) = t). The curve given as argument to the command is the function f(x)= \frac{x²}{4}, and the result is the derivative of that function: f'(x)= \frac{x}{2}.