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Given f (9) = 2. f' (9) 9. g (9) = -1, and g' (9) - 7, find the values of the following. (a) (b) (fg)' (9) Number (9) Number

Given f (9) = 2. f' (9) 9. g (9) = -1, and g' (9) - 7, find the values of the following. (a) (b) (fg)' (9) Number (9) Number

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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**Exercise on Derivatives and Functions** **Problem Statement:** Given the functions and derivatives: - \( f(9) = 2 \) - \( f'(9) = 9 \) - \( g(9) = -1 \) - \( g'(9) = 7 \) Find the values of the following expressions: (a) \( (fg)'(9) = \boxed{\text{Number}} \) (b) \( \left( \frac{f}{g} \right)'(9) = \boxed{\text{Number}} \) **Instructions:** - In part (a), use the product rule to find the derivative of the product of two functions at \( x = 9 \). - In part (b), use the quotient rule to find the derivative of the quotient of two functions at \( x = 9 \). **Additional Information:** - The product rule states \( (uv)' = u'v + uv' \). - The quotient rule states \( \left( \frac{u}{v} \right)' = \frac{u'v - uv'}{v^2} \). Calculate these expressions using the given values for the functions and their derivatives.
Transcribed Image Text:**Exercise on Derivatives and Functions** **Problem Statement:** Given the functions and derivatives: - \( f(9) = 2 \) - \( f'(9) = 9 \) - \( g(9) = -1 \) - \( g'(9) = 7 \) Find the values of the following expressions: (a) \( (fg)'(9) = \boxed{\text{Number}} \) (b) \( \left( \frac{f}{g} \right)'(9) = \boxed{\text{Number}} \) **Instructions:** - In part (a), use the product rule to find the derivative of the product of two functions at \( x = 9 \). - In part (b), use the quotient rule to find the derivative of the quotient of two functions at \( x = 9 \). **Additional Information:** - The product rule states \( (uv)' = u'v + uv' \). - The quotient rule states \( \left( \frac{u}{v} \right)' = \frac{u'v - uv'}{v^2} \). Calculate these expressions using the given values for the functions and their derivatives.
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