Find d²y 2/2 dx for the following function. y = 8x cos (x²)

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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### Problem Statement

Find the \(\frac{d^2y}{dx^2}\) for the following function.

\[ y = 8x \cos(x^2) \]

### Solution

Calculate the second-order derivative:

\[ \frac{d^2y}{dx^2} = \boxed{\phantom{answer}} \]

### Explanation:

1. The given function is \( y = 8x \cos(x^2) \).
2. To find the second derivative, we need to perform the differentiation twice. The steps to solve for \(\frac{d^2y}{dx^2}\) can be broken down methodically by first finding the first derivative \(\frac{dy}{dx}\) and then differentiating the result again to obtain the second derivative.
Transcribed Image Text:### Problem Statement Find the \(\frac{d^2y}{dx^2}\) for the following function. \[ y = 8x \cos(x^2) \] ### Solution Calculate the second-order derivative: \[ \frac{d^2y}{dx^2} = \boxed{\phantom{answer}} \] ### Explanation: 1. The given function is \( y = 8x \cos(x^2) \). 2. To find the second derivative, we need to perform the differentiation twice. The steps to solve for \(\frac{d^2y}{dx^2}\) can be broken down methodically by first finding the first derivative \(\frac{dy}{dx}\) and then differentiating the result again to obtain the second derivative.
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