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. Solution 
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. Analysis
Solution

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? 