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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Question
![**Derivative Rules:**
1. **Power Rule:**
\[
\frac{d}{dx}(x^n) = nx^{n-1}
\]
**Special Case of this:**
\[
\frac{d}{dx}\left(\sqrt{x}\right) = \frac{1}{2\sqrt{x}}
\]
2. **Addition/Subtraction Rule:**
\[
(u \pm v)' = u' \pm v'
\]
3. **Product Rule:**
\[
(uv)' = u'v + uv'
\]
4. **Quotient Rule:**
\[
\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}
\]
---
**Given:**
\[
f(x) = 6\sqrt{x} + \frac{8}{\sqrt{x}}
\]
**Calculate:**
\[
f'(x) = \boxed{}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8dbb38b-67db-4869-a2fb-b3f37c286b0c%2Ff8b45ad6-a9db-4aaa-a724-e2a3a61683ef%2F1u3uty4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Derivative Rules:**
1. **Power Rule:**
\[
\frac{d}{dx}(x^n) = nx^{n-1}
\]
**Special Case of this:**
\[
\frac{d}{dx}\left(\sqrt{x}\right) = \frac{1}{2\sqrt{x}}
\]
2. **Addition/Subtraction Rule:**
\[
(u \pm v)' = u' \pm v'
\]
3. **Product Rule:**
\[
(uv)' = u'v + uv'
\]
4. **Quotient Rule:**
\[
\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}
\]
---
**Given:**
\[
f(x) = 6\sqrt{x} + \frac{8}{\sqrt{x}}
\]
**Calculate:**
\[
f'(x) = \boxed{}
\]
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