Question

How do you find dy/dx given `x = t^2 - 2t` and `y = t^4 - 4t`?

Answer 1

`(dy)/(dx)=2(t^2+t+1)`

Explanation:

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

Here as `x=t^2-2t`, `(dx)/(dt)=2t-2=2(t-1)`

and as `y=t^4-4t`, `(dy)/(dt)=4t^3-4=4(t^3-1)=4(t-1)(t^2+t+1)`

Hence `(dy)/(dx)=(4(t-1)(t^2+t+1))/(2(t-1))=2(t^2+t+1)`