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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![### Calculating the Derivative Using the Quotient Rule
To calculate the derivative of the function below using the quotient rule:
\[ y = \frac{x^{10}}{\sqrt{x} + 5x^8} \]
Firstly, identify \( f(x) \) and \( g(x) \) from the function given. In this case:
\[ f(x) = \]
\[ g(x) = \]
Next, determine the derivatives of these functions:
\[ f'(x) = \]
\[ g'(x) = \]
Using these values, apply the quotient rule for derivatives:
\[ \left[ \frac{x^{10}}{\sqrt{x} + 5x^8} \right]' = \]
Fill in the respective derivatives to complete the calculation. The quotient rule is given by:
\[ y' = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2} \]
Place the values obtained from previous steps into this formula to find the final expression for the derivative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F461e6b03-e26d-48fc-aa6c-204c3b542fc6%2F5539192e-8af7-4f3f-9c00-16e94245e61d%2Fc4ze6a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Derivative Using the Quotient Rule
To calculate the derivative of the function below using the quotient rule:
\[ y = \frac{x^{10}}{\sqrt{x} + 5x^8} \]
Firstly, identify \( f(x) \) and \( g(x) \) from the function given. In this case:
\[ f(x) = \]
\[ g(x) = \]
Next, determine the derivatives of these functions:
\[ f'(x) = \]
\[ g'(x) = \]
Using these values, apply the quotient rule for derivatives:
\[ \left[ \frac{x^{10}}{\sqrt{x} + 5x^8} \right]' = \]
Fill in the respective derivatives to complete the calculation. The quotient rule is given by:
\[ y' = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2} \]
Place the values obtained from previous steps into this formula to find the final expression for the derivative.
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