The third variable is called the parameter More
precisely, a relation expressed between two variables x and y in the form
x = f(t), y = g (t) is said to be parametric form with t as a parameter In order to find derivative of function in such form, we have by chain rule dy
dt  = dy dx
dx dt
⋅
or
dy
dx  =
whenever
0
dy
dx
dt
dx
dt
dt


≠




Thus
dy
dx  =
( )
as
( ) and
( )
g t( )
dy
dx
g t
f t
f t
dt
dt
′


=
′
=
′


′

  [provided f′(t) ≠ 0]
Example 31 Find dy
dx , if x = a cos θ, y = a sin θ