How do you differentiate the following parametric equation: x(t)=cos^2t, y(t)=sint/t ?

1 Answer
Feb 12, 2017

dy/dx=-1/(2tsint)+1/(2t^2cost)

Explanation:

Given that the equations are
x(t)=cos^2t, y(t)=sint/t

The derivative of a parametric equation when in the form dy/dx can be re-written as (dy//dt)/(dx//dt)

For y(t) using quotient rule,
dy/dt=(tcost-sint)/t^2

Similarly, for x(t), using product rule,
dx/dt=-2costsint

So, the parametric differentiative turns to
{(tcost-sint)//t^2}/{-2sintcost}

Simplifying it shouldn't be a hassle to simplify.