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(b) g(x) = (1+4x)*(3+ x – x²)®

(b) g(x) = (1+4x)*(3+ x – x²)®

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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Question

find the derivative.

**Transcription** (b) \( g(x) = (1 + 4x)^5 (3 + x - x^2)^8 \) **Explanation** This function \( g(x) \) is expressed as the product of two terms raised to powers: 1. The first term is \( (1 + 4x)^5 \). This represents a binomial expression \( 1 + 4x \) raised to the fifth power, which involves expanding the expression into a polynomial. 2. The second term is \( (3 + x - x^2)^8 \). This is a trinomial expression \( 3 + x - x^2 \) raised to the eighth power. Expanding this requires applying the binomial theorem or similar methods for trinomial expansions. No graphs or diagrams are associated with this function in the given image. This equation provides a foundation for exploring polynomial multiplication, the binomial theorem, and algebraic manipulation. It's often used in calculus and algebra to demonstrate derivative rules or integration techniques.
Transcribed Image Text:**Transcription** (b) \( g(x) = (1 + 4x)^5 (3 + x - x^2)^8 \) **Explanation** This function \( g(x) \) is expressed as the product of two terms raised to powers: 1. The first term is \( (1 + 4x)^5 \). This represents a binomial expression \( 1 + 4x \) raised to the fifth power, which involves expanding the expression into a polynomial. 2. The second term is \( (3 + x - x^2)^8 \). This is a trinomial expression \( 3 + x - x^2 \) raised to the eighth power. Expanding this requires applying the binomial theorem or similar methods for trinomial expansions. No graphs or diagrams are associated with this function in the given image. This equation provides a foundation for exploring polynomial multiplication, the binomial theorem, and algebraic manipulation. It's often used in calculus and algebra to demonstrate derivative rules or integration techniques.
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