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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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![**Homework 5**
**Problem #3:**
Given the function:
\[ f(x) = 9x (11x^4 + \frac{47}{x+1}) \]
Find the derivative:
\[ f'(x) = \]
**Explanation:**
The task is to differentiate the function \( f(x) \), which is a product of two functions: \( 9x \) and \( (11x^4 + \frac{47}{x+1}) \). This requires applying the product rule of differentiation. The derivative will involve applying the sum and power rules, and simplifying the expression involving the quotient.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd390636-d92b-4083-92a5-4c40492431da%2F0b3826da-0969-4ccc-be6f-1b57b75a5f97%2Fd0dgglb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Homework 5**
**Problem #3:**
Given the function:
\[ f(x) = 9x (11x^4 + \frac{47}{x+1}) \]
Find the derivative:
\[ f'(x) = \]
**Explanation:**
The task is to differentiate the function \( f(x) \), which is a product of two functions: \( 9x \) and \( (11x^4 + \frac{47}{x+1}) \). This requires applying the product rule of differentiation. The derivative will involve applying the sum and power rules, and simplifying the expression involving the quotient.
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