Question

How do you differentiate the following parametric equation: `x(t)=cos^2t, y(t)=sin2t`?

Answer 1

`dy/dx = -2 cot2t`

Explanation:

`x(t) = cos^2 t`
differentiate wrt to t

`dx/dt = 2 (cost) d/dt(cost)`
`dx/dt = 2( cost) (-sint)`
`dx/dt = - sin2t`

`y(t) = sin2t`
Differentiate wrt to t
`dy/dt = 2 cos2t`

Using chain rule `dy/dx = dy/dt` x `dt/dx`

`dy/dt = 2 cost 2t` x `1/(-sin2t)`

`dy/dx = - 2 / (tan2t)`
`dy/dx = -2 cot 2t`