Question

How do you differentiate the following parametric equation: `x(t)=e^t-1/t, y(t)=1-t^2`?

Answer 1

Hi there!

Anytime you're given parametric equations to differentiate, you use the relationship whereby:

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

Explanation:

Let's start off by differentiating each equation separately, then combine the two afterwards!

Differentiating y with respect to t (dy/dt) we get:

`dy/dt = -2t`

Differentiating x with respect to t (dx/dt) we get:

`dx/dt = e^t - 1/t^2`

(If you're not sure how I got the `-1/t^2` from `1/t`... If you convert the `1/t` to `t^-1` and differentiate using the power rule, it comes out to `-t^-2` which is equivalent to `-1/t^2`)

Now putting everything together we get:

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

Hopefully this answers your question clearly! If you have any follow up questions, please feel free to ask! :)