1. Use appropriate differentiation technique(s) to compute f'(x) for each function below. Simplify your answers as much as possible. a. f(x) = x² sin (x) [Use the fact that sin(x) = cos(x)] b. f(x) = 6-7x 1+2x
1. Use appropriate differentiation technique(s) to compute f'(x) for each function below. Simplify your answers as much as possible. a. f(x) = x² sin (x) [Use the fact that sin(x) = cos(x)] b. f(x) = 6-7x 1+2x
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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![### Differentiation Exercise
**1. Use appropriate differentiation technique(s) to compute \( f'(x) \) for each function below. Simplify your answers as much as possible.**
#### a. \( f(x) = x^2 \sin(x) \)
Use the fact that \( \frac{d}{dx}\sin(x) = \cos(x) \).
#### b. \( f(x) = \frac{6 - 7x}{1 + 2x} \)
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**Instructions:**
- Apply the product rule for part (a). Remember, the product rule states that if you have a function \( u(x) \cdot v(x) \), then the derivative is \( u'(x) \cdot v(x) + u(x) \cdot v'(x) \).
- Apply the quotient rule for part (b). The quotient rule states that if you have a function \( \frac{u(x)}{v(x)} \), then the derivative is given by \( \frac{u'(x) \cdot v(x) - u(x) \cdot v'(x)}{[v(x)]^2} \).
These differentiation techniques will help you compute and simplify \( f'(x) \) for each function provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93dc20bf-0fea-4660-8028-43a1db35511d%2Ff077f537-9021-4433-ab74-e608b1ab1470%2Fttof1zo_processed.png&w=3840&q=75)
Transcribed Image Text:### Differentiation Exercise
**1. Use appropriate differentiation technique(s) to compute \( f'(x) \) for each function below. Simplify your answers as much as possible.**
#### a. \( f(x) = x^2 \sin(x) \)
Use the fact that \( \frac{d}{dx}\sin(x) = \cos(x) \).
#### b. \( f(x) = \frac{6 - 7x}{1 + 2x} \)
---
**Instructions:**
- Apply the product rule for part (a). Remember, the product rule states that if you have a function \( u(x) \cdot v(x) \), then the derivative is \( u'(x) \cdot v(x) + u(x) \cdot v'(x) \).
- Apply the quotient rule for part (b). The quotient rule states that if you have a function \( \frac{u(x)}{v(x)} \), then the derivative is given by \( \frac{u'(x) \cdot v(x) - u(x) \cdot v'(x)}{[v(x)]^2} \).
These differentiation techniques will help you compute and simplify \( f'(x) \) for each function provided.
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