Question

What is the derivative of `f(t) = (tcos^2t , t^2-t /sect )`?

Answer 1

`(dy)/(dx)=(cos^2t-tsin2t)/(2t-cost+tsint)`

Explanation:

To find derivative of a parmetric equation such as `f(t)=(x(t),y(t))`, we use formula `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

As `y(t)=tcos^2t`, we have `(dy)/(dt)=cos^2t+txx2costxx(-sint)`

= `cos^2t-txx2sintcost=cos^2t-tsin2t`

and as `x(t)=t^2-t/sect=t^2-tcost`

`(dx)/(dt)=2t-cost-txx(-sint)=2t-cost+tsint`

Hence `(dy)/(dx)=(cos^2t-tsin2t)/(2t-cost+tsint)`