Question

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

Answer 1

`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.