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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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 label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute. a. Let m(w) = 3w174". Find m'(w). b. Let h(t) = (sin(t) + cos(t))t*. Find h'(t). %3D 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
Transcribed Image Text: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 label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute. a. Let m(w) = 3w174". Find m'(w). b. Let h(t) = (sin(t) + cos(t))t*. Find h'(t). %3D 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
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