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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![**Find the derivative of the function.**
Given function:
\[ h(x) = 27 \sqrt[9]{x^2} - \frac{36}{\sqrt[9]{x}} \]
Derivative of the function:
\[ h'(x) = \]
**Note:** The box is meant for the expression of the derivative and the red “X” indicates that the expression currently in the box is incorrect.
**Explanation:**
- \(\sqrt[9]{x^2}\) denotes the 9th root of \(x^2\).
- \(\frac{36}{\sqrt[9]{x}}\) denotes the division of 36 by the 9th root of \(x\).
In order to determine \(h'(x)\), you'll need to apply the rules of differentiation to \(h(x)\).
If you encounter errors, verify each step, paying attention to the exponents and application of the chain rule if necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e0cd55c-6f84-412a-ac81-9a79eaea810f%2F967f72c2-f14c-4968-9e21-7ee53d220d67%2Fs8kf3z_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the derivative of the function.**
Given function:
\[ h(x) = 27 \sqrt[9]{x^2} - \frac{36}{\sqrt[9]{x}} \]
Derivative of the function:
\[ h'(x) = \]
**Note:** The box is meant for the expression of the derivative and the red “X” indicates that the expression currently in the box is incorrect.
**Explanation:**
- \(\sqrt[9]{x^2}\) denotes the 9th root of \(x^2\).
- \(\frac{36}{\sqrt[9]{x}}\) denotes the division of 36 by the 9th root of \(x\).
In order to determine \(h'(x)\), you'll need to apply the rules of differentiation to \(h(x)\).
If you encounter errors, verify each step, paying attention to the exponents and application of the chain rule if necessary.
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