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
9.) find derivative
![The given mathematical expression is:
\[ f(x) = \frac{6}{\sqrt{5x^2 + 4e^x + 3e^2}} \]
This function, \( f(x) \), is defined as the ratio of 6 to the square root of an expression in the denominator, which consists of 5 times \( x \) squared, plus 4 times the exponential function raised to the power of \( x \), plus 3 times the constant \( e \) squared.
Important Components:
- \( \sqrt{} \) denotes the square root.
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
- The expression inside the square root is \( 5x^2 + 4e^x + 3e^2 \).
This function is likely to be used in calculus or algebra for exploring properties like continuity, limits, or derivatives.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde916854-1188-4629-b15c-54b14230bd18%2F17a3b16a-a56e-4cf1-b313-7648d4269f71%2Fr8bdkfm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The given mathematical expression is:
\[ f(x) = \frac{6}{\sqrt{5x^2 + 4e^x + 3e^2}} \]
This function, \( f(x) \), is defined as the ratio of 6 to the square root of an expression in the denominator, which consists of 5 times \( x \) squared, plus 4 times the exponential function raised to the power of \( x \), plus 3 times the constant \( e \) squared.
Important Components:
- \( \sqrt{} \) denotes the square root.
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
- The expression inside the square root is \( 5x^2 + 4e^x + 3e^2 \).
This function is likely to be used in calculus or algebra for exploring properties like continuity, limits, or derivatives.
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