Find dy dx In (y²) = 4x + 5 - dy dx dy dx dy dx dy dx = = - = 2y -2y 2 K|N Y 2 У

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...
Question
**Differentiation Problem:**

**Objective:** Find \(\frac{dy}{dx}\).

**Equation Given:** 
\[
\ln(y^2) = 4x + 5
\]

**Options for \(\frac{dy}{dx}\):**

1. \(\frac{dy}{dx} = 2y\)

2. \(\frac{dy}{dx} = -2y\)

3. \(\frac{dy}{dx} = \frac{2}{y}\)

4. \(\frac{dy}{dx} = -\frac{2}{y}\) ⓘ

**Explanation:** 

The problem asks for the derivative \(\frac{dy}{dx}\) when the natural logarithm of \(y^2\) is equal to a linear function of \(x\). The correct answer is \(-\frac{2}{y}\), which has been indicated.
Transcribed Image Text:**Differentiation Problem:** **Objective:** Find \(\frac{dy}{dx}\). **Equation Given:** \[ \ln(y^2) = 4x + 5 \] **Options for \(\frac{dy}{dx}\):** 1. \(\frac{dy}{dx} = 2y\) 2. \(\frac{dy}{dx} = -2y\) 3. \(\frac{dy}{dx} = \frac{2}{y}\) 4. \(\frac{dy}{dx} = -\frac{2}{y}\) ⓘ **Explanation:** The problem asks for the derivative \(\frac{dy}{dx}\) when the natural logarithm of \(y^2\) is equal to a linear function of \(x\). The correct answer is \(-\frac{2}{y}\), which has been indicated.
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