Question

Consider r(t) = and g(t) = 8t³. evaluate d/dt(r(g(t)))

Answer 1

To evaluate d/dt(r(g(t))), substitute g(t) into r(t) and then take the derivative.

Step-by-step explanation:

To evaluate d/dt(r(g(t))), we first substitute g(t) into r(t) to get r(g(t)). Then we take the derivative of r(g(t)) with respect to t.

Let's break it down step by step:

1. Substitute g(t) into r(t): r(g(t)) = r(8t³)
2. Take the derivative of r(g(t)) with respect to t: d/dt(r(g(t))) = d/dr(8t³) * d/dt(8t³)
3. Simplify the derivative: d/dt(r(g(t))) = 3r² * 24t²