Question

Find the first and second derivative of the function defined by the parametric equation.

x = 3e and y= 3^3t - 1​

Answer 1

Explanation:

Given two parametric equations
`x(t)` and
`y(t)`, the first derivative can be found using the following equation:

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

In this problem,
`x(t) = 3e` and
`y(t) = 3^(3t) - 1`. Finding the derivative of each of these functions with respect to
`t` gives us the following:

`(dx)/(dt) = 0`

`(dy)/(dt) = 3^(3t + 1)\log{3}`

Because
`(dx)/(dt) = 0`, that means the function is a vertical line and has an infinite first derivative.