Suppose that functions f and g and their derivatives with respect X to x have the values shown to the right at x = 2 and x= 3. Find the derivatives with respect to x of the combinations below at the 2 given values of x. 3 a. 3f(x), x=2 e. f(g(x)), x=2 b. f(x) + g(x), x= 3 f. √f(x), x=2 c. f(x) g(x), x= 3 g. 1 g²(x) x=3 f(x) 8 1 g(x) 2 -2 d. f'(x) 15 x = 2 Зл f(x) g(x) h. √₁²(x)+g² (x), x=2 g'(x) -5 5
Suppose that functions f and g and their derivatives with respect X to x have the values shown to the right at x = 2 and x= 3. Find the derivatives with respect to x of the combinations below at the 2 given values of x. 3 a. 3f(x), x=2 e. f(g(x)), x=2 b. f(x) + g(x), x= 3 f. √f(x), x=2 c. f(x) g(x), x= 3 g. 1 g²(x) x=3 f(x) 8 1 g(x) 2 -2 d. f'(x) 15 x = 2 Зл f(x) g(x) h. √₁²(x)+g² (x), x=2 g'(x) -5 5
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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Can I ask for help with specifically the last four subparts? (e, f, g, h)
Transcribed Image Text:Suppose that functions f and g and their derivatives with respect
to x have the values shown to the right at x = 2 and x = 3. Find
the derivatives with respect to x of the combinations below at the
given values of x.
a. 3f(x), x = 2
e. f(g(x)), x=2
b. f(x) + g(x), x = 3
f. √f(x), x=2
g.
c. f(x) g(x), x= 3
1
g² (x)
1
X
x = 3
2
3
f(x)
8
1
d.
g(x)
2
- 2
f(x)
g(x)'
f'(x)
1
5
3π
x=2
g'(x)
- 5
5
h. √₁²(x)+g² (x), x=2
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Transcribed Image Text:e. The derivative of f(g(x)) with respect to x at x = 2 is -1.
(Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)
1
f. The derivative of √f(x) with respect to x at x = 2 is
20√/2
(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
1
g² (x)
(Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)
g. The derivative of
with respect to x at x = 3 is
5
4
h. The derivative of √1²(x) + g² (x) with respect to x at x = 2 is
21
(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
5√17
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