AP Calculus AB 3.1: Chain Rule

Practice AP Calculus questions on applying the chain rule to calculate derivatives of compositions of differentiable functions.

[Maximum number: 2]

Two particles, H and J, are moving along the x-axis. For $0 \leq t \leq 5$ , the position of particle H at

time t is given by $x_{H}(t)=e^{t^{2}-4 t}$ and the velocity of particle J at time t is given by

$v_{J}(t)=2 t\left(t^{2}-1\right)^{3}$ .

Find the velocity of particle H at time t=1. Show the work that leads to your answer.

A	Find the velocity of particle H at time t=1. Show the work that leads to your answer.
		$x_{H}{ }^{\prime}(t)=v_{H}(t)=(2 t-4) e^{t^{2}-4 t}$	Considers $x_{H}{ }^{\prime}$ Point 1 (P1)
		$x_{H}{ }^{\prime}(1)=v_{H}(1)=-2 e^{-3}$	Answer Point 2 (P2)
		Scoring Notes for Part A
		- P1 can be earned by presenting $x_{H}{ }^{\prime}(t), x_{H}{ }^{\prime}(1), x^{\prime}(t), x^{\prime}(1),(2 t-4) e^{t^{2}-4 t}$ , or $(2 \cdot 1-4) e^{1^{2}-4 \cdot 1}$ . - An unsupported answer of $-2 e^{-3}$ earns P2 but not P1.

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FUN-3.C—Calculate derivatives of compositions of differentiable functions question 1