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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PLEASE DO QUESTION 2
![Here is the transcription of the given functions, as might appear on an educational website:
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**Functions and Their Derivatives**
1. \( f(x) = x^4 \ln(x) \)
2. \( f(w) = \sqrt{4 + 2w - 9w^2 \, \sqrt[5]{7w + 2w^3 + w^5}} \)
3. \( h(z) = \frac{(1 + 7z^2)^3}{(2 + 3z + 4z^2)^4} \)
4. \( g(x) = \frac{\sqrt{1 + \sin(2x)}}{2x - \tan(x)} \)
5. \( h(t) = \frac{(9 - 3t)^{10}}{t^2 \sin(7t)} \)
6. \( y = \frac{3 + 8x}{(1 + 2x^2)^4} \cdot \frac{\cos(1-x)}{(5x + x^2)^7} \)
For problems 7 – 10, find the first derivative of the given function.
7. \( y = x \ln(x) \)
8. \( R(t) = (\sin(4t))^{6t} \)
9. \( h(w) = (6 - w^2)^{2+8w+w^3} \)
10. \( g(z) = z^{x^2} [3 + z]^{1-z^2} \)
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Each function presents an opportunity to practice differentiation techniques such as the product rule, quotient rule, chain rule, and logarithmic differentiation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F237d4048-a709-45b4-bafb-64f7e9c62b1d%2F6866ddd4-49c5-4f91-86ca-fb81590cc6bb%2F7l7879k.jpeg&w=3840&q=75)
Transcribed Image Text:Here is the transcription of the given functions, as might appear on an educational website:
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**Functions and Their Derivatives**
1. \( f(x) = x^4 \ln(x) \)
2. \( f(w) = \sqrt{4 + 2w - 9w^2 \, \sqrt[5]{7w + 2w^3 + w^5}} \)
3. \( h(z) = \frac{(1 + 7z^2)^3}{(2 + 3z + 4z^2)^4} \)
4. \( g(x) = \frac{\sqrt{1 + \sin(2x)}}{2x - \tan(x)} \)
5. \( h(t) = \frac{(9 - 3t)^{10}}{t^2 \sin(7t)} \)
6. \( y = \frac{3 + 8x}{(1 + 2x^2)^4} \cdot \frac{\cos(1-x)}{(5x + x^2)^7} \)
For problems 7 – 10, find the first derivative of the given function.
7. \( y = x \ln(x) \)
8. \( R(t) = (\sin(4t))^{6t} \)
9. \( h(w) = (6 - w^2)^{2+8w+w^3} \)
10. \( g(z) = z^{x^2} [3 + z]^{1-z^2} \)
---
Each function presents an opportunity to practice differentiation techniques such as the product rule, quotient rule, chain rule, and logarithmic differentiation.
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