Question

What is the derivative of `f(t) = (e^(t^2-1)-t, 2t^2-4t )`?

Answer 1

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

Explanation:

Derivative of a parametric function `f(t)=(x(t),y(t))` is given by `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`
As `y(t)=2t^2-4t`, `(dy)/(dt)=4t-4`

and as `x(t)=e^(t^2-1)-t`,, `(dx)/(dt)=e^(t^2-1)xx2t-1=2te^(t^2-1)-1`

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