Question

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

Answer 1

Answer:

Step-by-step explanation:

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

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

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:

$\frac{dx}{dt} = 0$

$\frac{dy}{dt} = 3^{3t + 1}\log{3}$

Because $\frac{dx}{dt} = 0$, that means the function is a vertical line and has an infinite first derivative.