Second derivative of parametric equation


First derivative


          Given a parametric equation:

                                  x = f(t) , y = g(t)

It is not difficult to find the first derivative by the formula:




Example 1

          If             x = t + cos t

                          y = sin t

          find the first derivative.






Second derivative


However it is not true to write the formula of the second derivative as the first derivative,

that is,




Example 2


If               x = t + cos t

                  y = sin t

  find the second derivative.












For more serious learner


          The formula for the second derivative of parametric equation is given by:



Can you prove this by following the steps in Example 2?