A student was asked to find the derivative of a complicated function. The function had the form Y = f(x) g(x)

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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hi could please answer this queestion im struggling on. pls dont take so loong thanks.

A student was asked to find the derivative of a complicated function. The function
had the form
Y =
f(x)
g(x)
They re-wrote the function to use the product rule and realized they needed to use
the chain rule for the derivatives of f(x) and g(x). Here is the first line of their
solution.
y′ = 5(1 + 2x)(2)(3x² − 5)−² + (1 + 2x)³ (−2)(3x² – 5)(6x)
-
State the mistake(s) they have made then correct the first line of the solution. Then
continue the solution to find the final expression for the derivative (it should be fully
factored and simplified and contain no negative exponents).
Transcribed Image Text:A student was asked to find the derivative of a complicated function. The function had the form Y = f(x) g(x) They re-wrote the function to use the product rule and realized they needed to use the chain rule for the derivatives of f(x) and g(x). Here is the first line of their solution. y′ = 5(1 + 2x)(2)(3x² − 5)−² + (1 + 2x)³ (−2)(3x² – 5)(6x) - State the mistake(s) they have made then correct the first line of the solution. Then continue the solution to find the final expression for the derivative (it should be fully factored and simplified and contain no negative exponents).
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