Use the properties of the derivative to find the following. r(t) = ti + 4tj + t²k, u(t) = 5ti + t²j + t³k (a) r'(t) i + 4j + (2t)k (b) __[2r(t) – u(t)] dt −3i + (8 − 2t)j + (4t−31²) k (c) [(3t)u(t)] 30ti + 9t²j + 12t³k (d) [r(t)u(t)] dt (e) [r(t) x u(t)] dt X
Use the properties of the derivative to find the following. r(t) = ti + 4tj + t²k, u(t) = 5ti + t²j + t³k (a) r'(t) i + 4j + (2t)k (b) __[2r(t) – u(t)] dt −3i + (8 − 2t)j + (4t−31²) k (c) [(3t)u(t)] 30ti + 9t²j + 12t³k (d) [r(t)u(t)] dt (e) [r(t) x u(t)] dt X
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Use the properties of the derivative to find the following.
r(t) = ti + 4tj + t²k, u(t) = 5ti + t²j + t³k
(a) r'(t)
i + 4j + (2t)k
d_[2r(t) – u(t)]
-
−3i + (8 − 2t)j + (4t − 31²) k
(b) [2r(t)
(c) [(3t)u(t)]
30ti + 9t²j + 12t³k
(d) [r(t). u(t)]
dt
(e) [r(t) x u(t)]
(f) dr(4t)
X
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F093e7116-3e01-49ad-9157-7a22a5caeb16%2F837ffae5-a145-42bf-bafd-06a81d04647f%2Fyw4nzuj_processed.png&w=3840&q=75)
Transcribed Image Text:Use the properties of the derivative to find the following.
r(t) = ti + 4tj + t²k, u(t) = 5ti + t²j + t³k
(a) r'(t)
i + 4j + (2t)k
d_[2r(t) – u(t)]
-
−3i + (8 − 2t)j + (4t − 31²) k
(b) [2r(t)
(c) [(3t)u(t)]
30ti + 9t²j + 12t³k
(d) [r(t). u(t)]
dt
(e) [r(t) x u(t)]
(f) dr(4t)
X
X
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