Question
Calculate $\mathbf{r}^{\prime}(t)$ and $\mathbf{r}^{\prime \prime}(t)$ for $\mathbf{r}(t)=\left\langle t, t^{2}, t^{3}\right\rangle$
Step 1
This is done by taking the derivative of each component of the vector with respect to $t$. So, we have $\mathbf{r}^{\prime}(t) = \frac{d}{dt}\left\langle t, t^{2}, t^{3}\right\rangle = \left\langle \frac{d}{dt}t, \frac{d}{dt}t^{2}, Show more…
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