For the following exercises, assume that f(x) and g(x) are both differentiable functions for all x. Find the derivative of each of the functions h(x). a) h(x) = x¹ f(x) ○ h'(x) = 4x³ + ƒ'(x) O h'(x) = 4r³ f(x) + x¹ƒ'(x) + x¹ƒ(1) Ⓒh'(x) = 4x³ f'(x) ○ h'(x) = x¹ f'(x) + 4x³ ƒ (x) O None of the above b) h(x) = f'(x)g'(x) 5 ○ h'(x) = {(f(x)g'(x) + g(x)f'(x)) O h'(x) = f(x)g(x) 5 1 ○ h'(x) = (f'(x) + g'(x)) h'(x) = f'(x)g(x) + f(x)g'(x) — 5f(x) g(x) 52
For the following exercises, assume that f(x) and g(x) are both differentiable functions for all x. Find the derivative of each of the functions h(x). a) h(x) = x¹ f(x) ○ h'(x) = 4x³ + ƒ'(x) O h'(x) = 4r³ f(x) + x¹ƒ'(x) + x¹ƒ(1) Ⓒh'(x) = 4x³ f'(x) ○ h'(x) = x¹ f'(x) + 4x³ ƒ (x) O None of the above b) h(x) = f'(x)g'(x) 5 ○ h'(x) = {(f(x)g'(x) + g(x)f'(x)) O h'(x) = f(x)g(x) 5 1 ○ h'(x) = (f'(x) + g'(x)) h'(x) = f'(x)g(x) + f(x)g'(x) — 5f(x) g(x) 52
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...
Related questions
Question

Transcribed Image Text:For the following exercises, assume that f(x) and g(x) are both differentiable
functions for all x. Find the derivative of each of the functions h(x).
4
a) h(x) = x¹ f(x)
○ h'(x) = 4x³ + ƒ'(x)
4
○ h'(x) = 4x³ f(x) + xª ƒ'(x) + xª ƒ(1)
○ h'(x) = 4x³ ƒ'(x)
○ h'(x) = x^ f'(x) + 4x³ƒ(x)
None of the above
b) h(x) =
O h'(x) =
=
f(x) g(x)
5
1
○ h'(x) = =— (ƒ(x)g'(x) + g(x)f'(x))
O h'(x)
f'(x) g'(x)
5
1
○ h'(x) = {{ (f'(x) + g'(x))
5
=
ƒ'(x)g(x) + f(x) g'(x) — 5ƒ(x) g(x)
5²
None of the above

Transcribed Image Text:c) h (x)
=
8f(x)
g(x) + 1
○ h'(x) =
○ h'(x) =
○ h'(x) =
=
○ h'(x) =
8 f'(x)
g'(x)
}
8 + f'(x)
(g'(x) + 1)²
where g(x) = -1 for all x.
8ƒ'(x)g'(x) +8f'(x) − 8ƒ(x)g(x)
(g'(x) + 1)²
None of the above
8g(x)ƒ'(x) +8ƒ'(x) — 8ƒ(x)g'(x)
(g(x) + 1)²
Nope. Try again. Score: 0%
CHECK ANSWER Attempt 3 of 3
!
Expert Solution
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