Question

Use the properties of the derivative to find the following. $\qquad r(t) = 9i + (t - 1)j$, $w(t) = t i + t^2 j + \frac{2}{3}t^3 k$ (a) $r'(t)$ $9i + j$ (b) $\frac{d}{dt}[w(t) - 2r(t)]$ $-17t + (2t - 2)j + 2t^2 k$ (c) $\frac{d}{dt}[(3t)r(t)]$ $54t i + (8t - 4)j$

          Use the properties of the derivative to find the following.
$\qquad r(t) = 9i + (t - 1)j$, $w(t) = t i + t^2 j + \frac{2}{3}t^3 k$
(a) $r'(t)$
$9i + j$
(b) $\frac{d}{dt}[w(t) - 2r(t)]$
$-17t + (2t - 2)j + 2t^2 k$
(c) $\frac{d}{dt}[(3t)r(t)]$
$54t i + (8t - 4)j$

Use the properties of the derivative to find the following.
r(t) = 9i + (t - 1)j, w(t) = t i + t^2 j + (2)/(3)t^3 k
(a) r'(t)
9i + j
(b) (d)/(dt)[w(t) - 2r(t)]
-17t + (2t - 2)j + 2t^2 k
(c) (d)/(dt)[(3t)r(t)]
54t i + (8t - 4)j

Added by Mercedes V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/15/2023

Step 1

Step 1: The derivative of r(t) with respect to t is given by: r'(t) = (9i + j) + (i + 2tj) Show more…

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Use the properties of the derivative to find the following.r(t) = 9ti + (t − 1)j, u(t) = ti + t2j + 23t3k Use the properties of the derivative to find the following =9+t-1t=++3 a,4e) +16 (b) dr -171+21-2+22 (c) 3tr(t] 54+8-4