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2.3 The product and quotient rules Activity 2.3.2. Use the product rule to answer each of the questions below. Throughout, be sure to carefully abel any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute. a. Let m(w) = 3w74". Find m'(w). b. Let h(t) = (sin(t) + cos(t))t*. Find h'(t). c. Determine the slope of the tangent line to the curve y = f(x) at the point where a = 1 if f is given by the rule f(x) = e sin(x). d. Find the tangent line approximation L(x) to the function y = g(x) at the point where a = -1 if g is given by the rule g(x) = (x² + x)2*. %3D %3D

2.3 The product and quotient rules Activity 2.3.2. Use the product rule to answer each of the questions below. Throughout, be sure to carefully abel any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute. a. Let m(w) = 3w74". Find m'(w). b. Let h(t) = (sin(t) + cos(t))t*. Find h'(t). c. Determine the slope of the tangent line to the curve y = f(x) at the point where a = 1 if f is given by the rule f(x) = e sin(x). d. Find the tangent line approximation L(x) to the function y = g(x) at the point where a = -1 if g is given by the rule g(x) = (x² + x)2*. %3D %3D

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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**Activity 2.3.2** Use the product rule to answer each of the questions below. Throughout, be sure to carefully label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute. a. Let \( m(w) = 3w^{17}4^w \). Find \( m'(w) \). b. Let \( h(t) = (\sin(t) + \cos(t))t^4 \). Find \( h'(t) \). c. Determine the slope of the tangent line to the curve \( y = f(x) \) at the point where \( a = 1 \) if \( f \) is given by the rule \( f(x) = e^x \sin(x) \). d. Find the tangent line approximation \( L(x) \) to the function \( y = g(x) \) at the point where \( a = -1 \) if \( g \) is given by the rule \( g(x) = (x^2 + x)2^x \).
Transcribed Image Text:**Activity 2.3.2** Use the product rule to answer each of the questions below. Throughout, be sure to carefully label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute. a. Let \( m(w) = 3w^{17}4^w \). Find \( m'(w) \). b. Let \( h(t) = (\sin(t) + \cos(t))t^4 \). Find \( h'(t) \). c. Determine the slope of the tangent line to the curve \( y = f(x) \) at the point where \( a = 1 \) if \( f \) is given by the rule \( f(x) = e^x \sin(x) \). d. Find the tangent line approximation \( L(x) \) to the function \( y = g(x) \) at the point where \( a = -1 \) if \( g \) is given by the rule \( g(x) = (x^2 + x)2^x \).
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