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8_murik_8 [283]
2 years ago
14

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

Mathematics
1 answer:
Sergeu [11.5K]2 years ago
6 0

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.

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