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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![### Calculus: Finding the Derivative of a Function
#### Problem Statement:
Find the derivative of the function.
\[ y = \frac{7}{\sqrt{x} + 2} \]
\[ y' = \boxed{ } \]
In this problem, we are given a function \( y = \frac{7}{\sqrt{x} + 2} \) and are asked to find its derivative with respect to \( x \). To solve this, we will apply the rules of differentiation, including the quotient rule and the chain rule.
- **Quotient Rule**: If \( y = \frac{u}{v} \), then \( y' = \frac{u'v - uv'}{v^2} \).
- **Chain Rule**: If a function is nested, such as \( f(g(x)) \), then the derivative is \( f'(g(x)) \cdot g'(x) \).
After differentiating, you will be able to input your answer in the provided boxed area.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d04d9e8-9cf4-4d61-b8ac-39958688637f%2Fec16ec7a-80b1-4aac-9aad-29c878e77bfb%2F3dweks.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus: Finding the Derivative of a Function
#### Problem Statement:
Find the derivative of the function.
\[ y = \frac{7}{\sqrt{x} + 2} \]
\[ y' = \boxed{ } \]
In this problem, we are given a function \( y = \frac{7}{\sqrt{x} + 2} \) and are asked to find its derivative with respect to \( x \). To solve this, we will apply the rules of differentiation, including the quotient rule and the chain rule.
- **Quotient Rule**: If \( y = \frac{u}{v} \), then \( y' = \frac{u'v - uv'}{v^2} \).
- **Chain Rule**: If a function is nested, such as \( f(g(x)) \), then the derivative is \( f'(g(x)) \cdot g'(x) \).
After differentiating, you will be able to input your answer in the provided boxed area.
---
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