Xfrog (Evaluation Version)

Derivatives of Parametric Equations

In Chapter 1 and Appendix A, I talked about how the slope corresponded to a derivative and how that can be thought of as "the change in y with respect to x". Now I have given you parametric equations as functions of t, so it might appear that you need something different. It's actually quite easy. Both x and y change with respect to the common parameter t. You can compute the derivative, as shown in Equation 3.3.

(3.3) The derivative of a parametric equation. 

In most of the remaining chapters, the parametric equations will be polynomial functions of t, so derivatives can easily be computed as described in Appendix A. For clarity, Equation 3.4 shows how this is done for a simple line. You will see more interesting examples when I begin to talk about slopes on a Bezier curve.

(3.4) The derivative of a line using a parametric equation.