Use the appropriate Product Rule to evaluate the derivative, where $$r_1(t) = \langle -7t, -2, -t^4 \rangle, r_2(t) = \langle 4, e^t, -9 \rangle$$ $$\frac{d}{dt}(r_1(t) \cdot r_2(t)) = \boxed{\phantom{}}$$
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The Product Rule for the dot product of two vector functions $r_1(t)$ and $r_2(t)$ is given by: $$\frac{d}{dt}(r_1(t) \cdot r_2(t)) = r_1'(t) \cdot r_2(t) + r_1(t) \cdot r_2'(t)$$ First, let's find the derivatives of $r_1(t)$ and $r_2(t)$. Given $r_1(t) = \langle Show more…
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