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
![**Problem Statement:**
Find the first derivative of \( y = 9e^{-10x^7+21} \).
\[ \frac{dy}{dx} = \]
**Instructions:**
To solve this problem, apply the chain rule. The expression is of the form \( y = a \cdot e^{f(x)} \), where \( a = 9 \) and \( f(x) = -10x^7 + 21 \). Calculate the derivative of the exponent and multiply it by the original function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc4bd04-a070-4f0a-8c81-81114a590c8c%2Ffe6802cd-f005-42de-97d7-d6844edc32d4%2Fqtnmoph_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the first derivative of \( y = 9e^{-10x^7+21} \).
\[ \frac{dy}{dx} = \]
**Instructions:**
To solve this problem, apply the chain rule. The expression is of the form \( y = a \cdot e^{f(x)} \), where \( a = 9 \) and \( f(x) = -10x^7 + 21 \). Calculate the derivative of the exponent and multiply it by the original function.

Transcribed Image Text:The problem presents the function \( f(x) = \left( \frac{x+2}{x+5} \right)^9 \).
The task is to find the derivative, denoted as \( f'(x) \).
Feel free to apply the chain rule and quotient rule of differentiation to solve for \( f'(x) \).
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