3 Find f'(x)given f(x) = x/x – 4x – 7x %3D

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 \( f'(x) \) given \( f(x) = x \sqrt{x} - 4x^3 - 7x \).

### Explanation

In this problem, we are asked to find the derivative of the function \( f(x) \). The function given is a combination of various terms:

\[ f(x) = x \sqrt{x} - 4x^3 - 7x \]

Here, \( x \sqrt{x} \) is a term involving a product of \( x \) and a square root, \( -4x^3 \) is a cubic term multiplied by a constant, and \( -7x \) is a linear term multiplied by a constant.

To solve this, apply the rules of differentiation to each term individually.
Transcribed Image Text:### Problem Statement Find \( f'(x) \) given \( f(x) = x \sqrt{x} - 4x^3 - 7x \). ### Explanation In this problem, we are asked to find the derivative of the function \( f(x) \). The function given is a combination of various terms: \[ f(x) = x \sqrt{x} - 4x^3 - 7x \] Here, \( x \sqrt{x} \) is a term involving a product of \( x \) and a square root, \( -4x^3 \) is a cubic term multiplied by a constant, and \( -7x \) is a linear term multiplied by a constant. To solve this, apply the rules of differentiation to each term individually.
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