Question

How do you differentiate the following parametric equation: `x(t)=(t+1)e^t, y(t)= t-e^(t-1)`?

Answer 1

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

Explanation:

In parametric form of equations, `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

Here `x(t)=(t+1)e^t` and therefore

`(dx)/(dt)=e^t+(t+1)e^t=(t+2)e^t`

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

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