7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te2t), g(t) = (-e2", 1– t²), for t e R. Also consider the function s: (0, 00) → R given by s(t) In(t) for t > 0. 2 (a) Find (f o s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.
7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te2t), g(t) = (-e2", 1– t²), for t e R. Also consider the function s: (0, 00) → R given by s(t) In(t) for t > 0. 2 (a) Find (f o s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.
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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
Transcribed Image Text:7.
Consider the functions f, g: R → R² given by:
f(t) = (t(2t – 3), te2t),
g(t) = (-e2“, 1 – t²),
for t E R.
In(t)
Also consider the function s: (0, 0) → R given by s(t)
for t > 0.
2
(a)
Find (f o s)'(t), for t > 0.
(b)
Find (f g)'(t), for t e R.
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