2. Vector-Valued Functions

Derivatives Of Vector Functions — Quiz

Test your understanding of derivatives of vector functions with 5 practice questions.

Practice Questions

Question 1

Let $\mathbf{r}(t) = \langle t^2, \sin(t), e^{t} \rangle$. What is $\mathbf{r}'(t)$?

Question 2

If $\mathbf{r}(t) = \langle 3t^3, e^{2t}, \ln(t) \rangle$, find the value of $\mathbf{r}'(1)$.

Question 3

Consider $\mathbf{r}(t) = \langle \cos(t), \sin(t), t^2 \rangle$. What is the unit tangent vector $\hat{T}(t)$ at $t = \frac{\pi}{4}$?

Question 4

Let $\mathbf{r}(t) = \langle t, t^2, t^3 \rangle$. What is the second derivative $\mathbf{r}''(t)$?

Question 5

Suppose $\mathbf{r}(t) = \langle e^t, \sin(t), \cos(t) \rangle$. What is the length of the velocity vector $\|\mathbf{r}'(t)\|$ at $t = 0$?