AP Calculus BC 9.4 Vector Derivatives Overview

Differentiate vector-valued position functions component by component and evaluate the resulting velocity vector at a specified time.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

CHA-3.H—Calculate derivatives of vector-valued functions

[Maximum number: 1]

For time t>0, the position of a particle moving in the x y-plane is given by the vector $\left\langle\frac{1}{t}, e^{3 t}\right\rangle$ . What is the velocity vector of the particle at time t=2 ?

$\left\langle\frac{1}{2}, e^{6}\right\rangle$

$\left\langle\frac{1}{4}, e^{6}\right\rangle$

$\left\langle\frac{1}{4}, 3 e^{6}\right\rangle$

$\left\langle-\frac{1}{4}, e^{6}\right\rangle$

$\left\langle-\frac{1}{4}, 3 e^{6}\right\rangle$

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Covered syllabus points

9.4 Defining and Differentiating Vector-Valued Functions question 1