4.14 Derivatives of Functions In Parametric Form
THEOREM : If x = f ( t ) and
y = y ( t ) are two derivable functions
of t such that y is defined as a function of x, then
=
Example 65 If x = at2 and y = 2 at
Find ![](Image685.gif)
Solution : x = at2
= 2 at and y = 2 at
= 2a
= ![](Image689.gif)
= ![](Image690.gif)
= ![](Image691.gif)
Example 66 If
![](Image693.gif)
= ![](Image695.gif)
and
y = ![](Image697.gif)
= ![](Image698.gif)
=
![](Image699.gif)
=
= ![](Image701.gif)
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