Homework Help is Here – Start Your Trial Now!
Math
Calculus
Determine r' (x) if r(x) = (arccos(x)) ¹0. Select the correct answer below: r'(x) = 10(arccos(x))⁹ -10(arccos(x))⁹ ²-1 -10(arccos(x))⁹ O r'(x) = r'(x) = O r'(x) = O r'(x) = 10(arccos(x))⁹ √1-x² -x² 10

Determine r' (x) if r(x) = (arccos(x)) ¹0. Select the correct answer below: r'(x) = 10(arccos(x))⁹ -10(arccos(x))⁹ ²-1 -10(arccos(x))⁹ O r'(x) = r'(x) = O r'(x) = O r'(x) = 10(arccos(x))⁹ √1-x² -x² 10

Calculus: Early Transcendentals
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...
See similar textbooks
Question
Need help
### Problem Statement Determine \( r'(x) \) if \( r(x) = \left( \arccos(x) \right)^{10} \). ### Choices Select the correct answer below: - \(\bigcirc\) \( r'(x) = 10 (\arccos(x))^9 \) - \(\bigcirc\) \( r'(x) = \frac{-10 (\arccos(x))^9}{\sqrt{x^2 - 1}} \) - \(\bigcirc\) \( r'(x) = \frac{-10 (\arccos(x))^9}{\sqrt{1 - x^2}} \) - \(\bigcirc\) \( r'(x) = \frac{10 (\arccos(x))^9}{\sqrt{1 - x^2}} \) - \(\bigcirc\) \( r'(x) = \left( \frac{-1}{\sqrt{1 - x^2}} \right)^{10} \) ### Instructions To determine the correct expression for the derivative \( r'(x) \) of the given function \( r(x) \), apply the chain rule of differentiation. Evaluate each option and select the one that corresponds correctly to the derivative of \( r(x) = \left( \arccos(x) \right)^{10} \). ### Additional Notes - When using the chain rule, recall that if \( f(g(x)) \) is a composite function, then \( \frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x) \). - For the function \( r(x) = \left( \arccos(x) \right)^{10} \): - Identify the outer function \( f(u) = u^{10} \) where \( u = \arccos(x) \). - Compute the derivative of the outer function: \( f'(u) = 10u^9 \). - Identify the inner function \( g(x) = \arccos(x) \) and compute its derivative. Finally, combine the results to find \( r'(x) \).
Transcribed Image Text:### Problem Statement Determine \( r'(x) \) if \( r(x) = \left( \arccos(x) \right)^{10} \). ### Choices Select the correct answer below: - \(\bigcirc\) \( r'(x) = 10 (\arccos(x))^9 \) - \(\bigcirc\) \( r'(x) = \frac{-10 (\arccos(x))^9}{\sqrt{x^2 - 1}} \) - \(\bigcirc\) \( r'(x) = \frac{-10 (\arccos(x))^9}{\sqrt{1 - x^2}} \) - \(\bigcirc\) \( r'(x) = \frac{10 (\arccos(x))^9}{\sqrt{1 - x^2}} \) - \(\bigcirc\) \( r'(x) = \left( \frac{-1}{\sqrt{1 - x^2}} \right)^{10} \) ### Instructions To determine the correct expression for the derivative \( r'(x) \) of the given function \( r(x) \), apply the chain rule of differentiation. Evaluate each option and select the one that corresponds correctly to the derivative of \( r(x) = \left( \arccos(x) \right)^{10} \). ### Additional Notes - When using the chain rule, recall that if \( f(g(x)) \) is a composite function, then \( \frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x) \). - For the function \( r(x) = \left( \arccos(x) \right)^{10} \): - Identify the outer function \( f(u) = u^{10} \) where \( u = \arccos(x) \). - Compute the derivative of the outer function: \( f'(u) = 10u^9 \). - Identify the inner function \( g(x) = \arccos(x) \) and compute its derivative. Finally, combine the results to find \( r'(x) \).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS