Question

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

Answer 1

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

Explanation:

The derivative of a parametric equation `f(t)=(x(t),y(t))` is given by `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

As `x(t)=te^(-t)`, `(dx)/(dt)=e^(-t)+txx(-e^(-t))=e^(-t)(1-t)`

and as `y=e^t/t`, `(dy)/(dt)=(te^t-e^txx1)/t^2`

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

and `(dy)/(dx)=e^t/t^2(t-1)xx1/(e^(-t)(1-t))`

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