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Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate. y = (3-x²) (x³ - 4x+2) a. Apply the Product Rule. Let u = (3-x2) and v = (x³-4x+2). a (uv) = (3-x²) (O + (x³ - 4x+2) O %3D

Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate. y = (3-x²) (x³ - 4x+2) a. Apply the Product Rule. Let u = (3-x2) and v = (x³-4x+2). a (uv) = (3-x²) (O + (x³ - 4x+2) O %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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The task is to find the derivative \( y' \) by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate. Given: \[ y = (3 - x^2)(x^3 - 4x + 2) \] **a. Apply the Product Rule.** Let \( u = (3 - x^2) \) and \( v = (x^3 - 4x + 2) \). To find the derivative using the Product Rule: \[ \frac{d}{dx}(uv) = (3 - x^2)\text{(derivative of \( v \))} + (x^3 - 4x + 2)\text{(derivative of \( u \))} \] There are editable fields to fill in the derivatives of \( u \) and \( v \). **Instructions:** Enter your answer in the edit fields and then click "Check Answer." **Progress Indicator:** There is a progress bar showing "2 parts remaining." **Additional tools:** There is a "Clear All" button to reset the input fields.
Transcribed Image Text:The task is to find the derivative \( y' \) by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate. Given: \[ y = (3 - x^2)(x^3 - 4x + 2) \] **a. Apply the Product Rule.** Let \( u = (3 - x^2) \) and \( v = (x^3 - 4x + 2) \). To find the derivative using the Product Rule: \[ \frac{d}{dx}(uv) = (3 - x^2)\text{(derivative of \( v \))} + (x^3 - 4x + 2)\text{(derivative of \( u \))} \] There are editable fields to fill in the derivatives of \( u \) and \( v \). **Instructions:** Enter your answer in the edit fields and then click "Check Answer." **Progress Indicator:** There is a progress bar showing "2 parts remaining." **Additional tools:** There is a "Clear All" button to reset the input fields.
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