Question

What is the derivative of `f(t) = (tsint , t^2-t tant )`?

Answer 1

`(dy)/(dx)=(2t-tant-tsec^2t)/(sint+tcost)`

Explanation:

For parametric form of equation, `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`.

Here as `x=tsint`, `(dx)/(dt)=1xxsint+tcost=sint+tcost`
(using product rule)

and as `y=t^2-t tant`, `(dy)/(dt)=2t-tant-tsec^2t`
(using product rule)

hence `(dy)/(dx)=(2t-tant-tsec^2t)/(sint+tcost)`