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 2 g(x) X x = 3 2 3 f(x) 8 1 g(x) 2 - 1 d. f'(x) 1 T f(x) g(x)' h. √r²(x)+g² (x), x=2 x=2 g'(x) - 3 3

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 37CR
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Question
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.
1
2
g² (x)
c. f(x) g(x), x= 3
"
X
x=3
2
3
f(x) g(x)
2
8
1
d.
- 1
f(x)
g(x)'
f'(x)
1
7
T
x=2
g'(x)
- 3
3
h. √r²(x)+g²(x), x=2
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. 1 2 g² (x) c. f(x) g(x), x= 3 " X x=3 2 3 f(x) g(x) 2 8 1 d. - 1 f(x) g(x)' f'(x) 1 7 T x=2 g'(x) - 3 3 h. √r²(x)+g²(x), x=2
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