Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
Solution to question 2 (d),(e),(f) please
Question 1
Let f be a differentiable function. We are given the following values of f and f'
f(x)
f'(x)
1
4
1
2
4
2
4
1
4
Consider the functions g, h, and k defined by
g(x) = f(x²) h(x) =
f(x)
2:2
k(x) = 3(f(x))³ — √√ f(x)'
l(x) = f(f(x) - 2) — f(x)g(x)
Find the following values. Show all necessary work:
(a) g'(2)
(b) h'(1)
Question 2
(c) k'(4)
(d) l'(2)
(d) f(x)
arcsec(3x)
cos(x)
(e) f(x)=sin(2 cos(arccot x))
3
Find f'(x). Do not simplify your answer.
(a) f(x) = arcsin (log2(2x+1)+x)
(b) f(x)=-5x2 arctan (ln x)
(c) f(x) = ((x² - 1)5 - √π + 1)³
Question 3
Consider the curve x sin(xy - y2) = x − 1.
dy
dx
(f) f(x) = log (1+) In (sec²(x)+1)
dx
(b)
dy
expand button
Transcribed Image Text:Question 1 Let f be a differentiable function. We are given the following values of f and f' f(x) f'(x) 1 4 1 2 4 2 4 1 4 Consider the functions g, h, and k defined by g(x) = f(x²) h(x) = f(x) 2:2 k(x) = 3(f(x))³ — √√ f(x)' l(x) = f(f(x) - 2) — f(x)g(x) Find the following values. Show all necessary work: (a) g'(2) (b) h'(1) Question 2 (c) k'(4) (d) l'(2) (d) f(x) arcsec(3x) cos(x) (e) f(x)=sin(2 cos(arccot x)) 3 Find f'(x). Do not simplify your answer. (a) f(x) = arcsin (log2(2x+1)+x) (b) f(x)=-5x2 arctan (ln x) (c) f(x) = ((x² - 1)5 - √π + 1)³ Question 3 Consider the curve x sin(xy - y2) = x − 1. dy dx (f) f(x) = log (1+) In (sec²(x)+1) dx (b) dy
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