Find f'(x) and simplify. X X-19 f(x) = Which of the following shows the correct application of the quotient rule? O A. O B. O C. O D. f'(x) = (x)(1)(x-19) (1) [x - 191² (x-19)(1)-(x)(1) [x - 191² (x)(1)(x-19) (1) [x]² (x-19)(1)-(x)(1) [x]²

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question
**Topic: Applying the Quotient Rule in Calculus**

**Objective:** Find \( f'(x) \) and simplify.

Given the function:
\[ f(x) = \frac{x}{x - 19} \]

**Choose the correct application of the quotient rule:**

**Options:**

**A.** \(\frac{(x)(1) - (x - 19)(1)}{[x - 19]^2}\)

**B.** \(\frac{(x - 19)(1) - (x)(1)}{[x - 19]^2}\)

**C.** \(\frac{(x)(1) - (x - 19)(1)}{[x]^2}\)

**D.** \(\frac{(x - 19)(1) - (x)(1)}{[x]^2}\)

**Calculate \( f'(x) = \) [input box]**

---

Ensure the correct application of the quotient rule in differentiating functions expressed as \(\frac{u(x)}{v(x)}\), where:
\[ u(x) = x \]
\[ v(x) = x - 19 \]

The quotient rule states:
\[ f'(x) = \frac{v(x)u'(x) - u(x)v'(x)}{[v(x)]^2} \]

Select the option that fits this form from those provided.
Transcribed Image Text:**Topic: Applying the Quotient Rule in Calculus** **Objective:** Find \( f'(x) \) and simplify. Given the function: \[ f(x) = \frac{x}{x - 19} \] **Choose the correct application of the quotient rule:** **Options:** **A.** \(\frac{(x)(1) - (x - 19)(1)}{[x - 19]^2}\) **B.** \(\frac{(x - 19)(1) - (x)(1)}{[x - 19]^2}\) **C.** \(\frac{(x)(1) - (x - 19)(1)}{[x]^2}\) **D.** \(\frac{(x - 19)(1) - (x)(1)}{[x]^2}\) **Calculate \( f'(x) = \) [input box]** --- Ensure the correct application of the quotient rule in differentiating functions expressed as \(\frac{u(x)}{v(x)}\), where: \[ u(x) = x \] \[ v(x) = x - 19 \] The quotient rule states: \[ f'(x) = \frac{v(x)u'(x) - u(x)v'(x)}{[v(x)]^2} \] Select the option that fits this form from those provided.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education