Question

What is the derivative of `f(t) = (2t-3te^t, 2t^2-t )`?

Answer 1

`(df)/(dx)=(4t-1)/(2-3e^t-3te^t)`

Explanation:

In a parametric equation `f(t)=(x(t),y(t))`, the derivative `(df)/(dx)=((dy)/(dt))/((dy)/(dt))`

Here we have `f(t)=(2t-3te^t,2t^2-t)`

As `x(t)=2t-3te^t`, `(dx)/(dt)=2-3e^t-3te^t`

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

and hence `(df)/(dx)=(4t-1)/(2-3e^t-3te^t)`