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dp Find dx given p(x) = (sin?(3x))(3x²-4*)

dp Find dx given p(x) = (sin?(3x))(3x²-4*)

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 \(\frac{dp}{dx}\) given \(p(x) = (\sin^2(3x))(3x^2 - 4^x)\). --- Here, we are tasked with finding the derivative of the function \(p(x)\), which is a product of two expressions: \((\sin^2(3x))\) and \((3x^2 - 4^x)\). To solve this problem, one would typically use the product rule of differentiation, which states that if you have a product of two functions \(u(x)\) and \(v(x)\), the derivative is given by: \[ \frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x) \] Hence, the approach involves finding the derivatives of the individual components and applying the product rule.
Transcribed Image Text:Find \(\frac{dp}{dx}\) given \(p(x) = (\sin^2(3x))(3x^2 - 4^x)\). --- Here, we are tasked with finding the derivative of the function \(p(x)\), which is a product of two expressions: \((\sin^2(3x))\) and \((3x^2 - 4^x)\). To solve this problem, one would typically use the product rule of differentiation, which states that if you have a product of two functions \(u(x)\) and \(v(x)\), the derivative is given by: \[ \frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x) \] Hence, the approach involves finding the derivatives of the individual components and applying the product rule.
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