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...
Related questions
Question
6
![**Question 6**
Differentiate the function
\[
f(x) = \frac{\sqrt{e^{-x^2} + x + 1}}{x^3 - 1}
\]
Options:
- \[ \frac{\left( -2x^4 - 3x^2 + 2x \right) e^{-x^2} - 2x^3 - 3x^2 - 1}{(x^3 - 1)^2} \]
- \[ \frac{\left( -2x^4 - 3x^2 + 2x \right) e^{-x^2}}{(x^3 - 1)^2} \]
- \[ \frac{-2x^3 + 3x^2 + 1}{(x^3 - 1)^2} \]
- \[ \frac{2xe^{-x^2} - 2x^3 - 3x^2 - 1}{(x^3 - 1) \sqrt{e^{-x^2} + x + 1}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8713e9b-73ac-4e4f-a322-df330d573c40%2Fcd1e7483-f30f-4a3f-9b7b-6ac143c4db30%2Fnj07hqp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6**
Differentiate the function
\[
f(x) = \frac{\sqrt{e^{-x^2} + x + 1}}{x^3 - 1}
\]
Options:
- \[ \frac{\left( -2x^4 - 3x^2 + 2x \right) e^{-x^2} - 2x^3 - 3x^2 - 1}{(x^3 - 1)^2} \]
- \[ \frac{\left( -2x^4 - 3x^2 + 2x \right) e^{-x^2}}{(x^3 - 1)^2} \]
- \[ \frac{-2x^3 + 3x^2 + 1}{(x^3 - 1)^2} \]
- \[ \frac{2xe^{-x^2} - 2x^3 - 3x^2 - 1}{(x^3 - 1) \sqrt{e^{-x^2} + x + 1}} \]
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