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Find the first derivative of y = dy dx = 9e-10x²+21

Find the first derivative of y = dy dx = 9e-10x²+21

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
**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:**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.
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 \( f'(x) \).
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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