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
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,...
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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbe47654-762f-4eea-844b-6a49397579c0%2F4b87733e-d448-4063-9fc2-a08d5b719023%2Fjajsepd_processed.png&w=3840&q=75)
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.
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