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Working with the function f(x) =x · sin x 10 Check all of the boxes to indicate the derivative rules you need to use to find f'(x). In the table below, state the two functions in the product, u(x) and v(x), and determine u'(x) and v'(x).

Working with the function f(x) =x · sin x 10 Check all of the boxes to indicate the derivative rules you need to use to find f'(x). In the table below, state the two functions in the product, u(x) and v(x), and determine u'(x) and v'(x).

Calculus: Early Transcendentals
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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Combining Derivative Rules (Select all that apply.) Working with the function f(x) sin x =x: 10 Constant Rule Power Rule Check all of the boxes to indicate the derivative rules you need to use to find f'(x). Exponential Function Rule Constant Multiple of a Function Rule In the table below, state the two functions in the product, u(x) and v(x), and determine u'(x) and v'(x). Sum/Difference of Functions Rule Trig Function Rule Product of Functions Rule Label Function Derivatives Quotient of Functions Rule u(x) v(x) Use your work from the table to calculate f'(x) and put your response in the box to the right.
Transcribed Image Text:Combining Derivative Rules (Select all that apply.) Working with the function f(x) sin x =x: 10 Constant Rule Power Rule Check all of the boxes to indicate the derivative rules you need to use to find f'(x). Exponential Function Rule Constant Multiple of a Function Rule In the table below, state the two functions in the product, u(x) and v(x), and determine u'(x) and v'(x). Sum/Difference of Functions Rule Trig Function Rule Product of Functions Rule Label Function Derivatives Quotient of Functions Rule u(x) v(x) Use your work from the table to calculate f'(x) and put your response in the box to the right.
Expert Solution
Step 1 Considering the two functions in the product u(x) and v(x)-

ux=xvx=sinx 

Differentiating w.r.t 'x' in u(x) and v(x) to both the sides-

u'x=1v'x=cosx

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