I need help solving this chain rule problem. I tried to solve it, but I'm a little confused on how to continue The image contains a step-by-step differentiation process using the chain rule and quotient rule. Here's a transcription and explanation:1. **Starting Expression:** \[ y = \left( \frac{x}{x+3} \right)^{1/2} = u^{1/2} \]2. **Substitution:** \[ u = \frac{x}{x+3} \]3. **Functions Definition:** \[ f(u) = u^{1/2} \quad g(x) = \frac{x}{x+3} \]4. **Expression for y:** \[ y = \left( \frac{x}{x+3} \right)^{1/2} \]5. **Derivative Start:** \[ y' = \frac{d}{dx} \left( \left( \frac{x}{x+3} \right)^{1/2} \right) \]6. **Chain Rule Application:** \[ y' = \frac{1}{2} \left( u \right)^{-1/2} \cdot \frac{d}{dx} \left( \frac{x}{x+3} \right) \] - Use the quotient rule for \(\frac{x}{x+3}\).7. **Quotient Rule Application:** \[ y' = \frac{1}{2} \cdot u^{-1/2} \cdot \frac{(x+3)(1) - (x)(1)}{(x+3)^2} \]8. **Simplified Derivative:** \[ y' = \frac{1}{2} \cdot \left( \frac{x}{x+3} \right)^{-1/2} \cdot \frac{3}{(x+3)^2} \]9. **Final Simplified Form:** \[ y' = \frac{1}{2} \cdot \frac{1}{\sqrt{\frac{x}{x+3}}} \cdot \frac{3}{(x+3)^2} \] \[ y' = \frac{3}{2} \cdot \frac{1}{\ **Problem Statement:**Find the derivative of the function.\[ y = \sqrt{\frac{x}{x + 3}} \]**Explanation:**In this problem, we are asked to find the derivative of the function \( y \), which is defined as the square root of the fraction \(\frac{x}{x+3}\). To solve this, we apply the chain rule and quotient rule for derivatives. 1. **Chain Rule:** - If \( y = \sqrt{u} \), then \( \frac{dy}{du} = \frac{1}{2\sqrt{u}} \).2. **Quotient Rule**: - For a function \( u = \frac{f(x)}{g(x)} \), the derivative \( \frac{du}{dx} = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2} \).Using these rules will help find the derivative for more complex functions like the given one.

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Answered: Find the derivative of the function. y…

Math

Calculus

Find the derivative of the function. y = Xx x + 3

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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