Question

What is the derivative of `f(t) = (t^3-e^(3t-1) , t-e^t )`?

Answer 1

`(1-e^t)/(3t^2-3e^(3t-1))`

Explanation:

This is a parametric function where `x=t^3-e^(3t-1)` and `y=t-e^t`

and `(dy)/(dt)=1-e^t` and `(dx)/(dt)=3t^2-3e^(3t-1)`

Hence `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

= `(1-e^t)/(3t^2-3e^(3t-1))`