Question

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

Answer 1

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

Explanation:

When we have parametric equations, `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))`

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

and as `x=tant-sect`, `(dx)/(dt)=sec^2t-sect tant`

and `(dy)/(dx)=(e^t-1)/(sec^2t-sect tant)`