Sometimes the equation of a curve is not be given in Cartesian form y = f ( x ) but in parametric form: x = h ( t ) , y = g ( t ) . In this Section we see how to calculate the derivative d y d x from a knowledge of the so-called parametric derivatives d x d t and d y d t . We then extend this to the determination of the second derivative d 2 y d x 2 .

Parametric functions arise often in particle dynamics in which the parameter t represents the time and ( x ( t ) , y ( t ) ) then represents the position of a particle as it varies with time.


Learning Outcomes

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