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In 5 7x 78. y = log5V3x + 2

In 5 7x 78. y = log5V3x + 2

Calculus: Early Transcendentals
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

Find the derivative of y with respect to the given independent variable and show steps and formulas used in order. 

**Equation 78:** \( y = \log_5 \sqrt{\left( \frac{7x}{3x + 2} \right)^{\ln 5}} \) **Explanation:** This mathematical expression defines the function \( y \) in terms of \( x \). Here's a breakdown: - **\( \log_5 \)**: This denotes a logarithm with base 5. - **Square Root**: The expression inside the square root is raised to a certain power, and then the square root is taken. - **Fraction \(\frac{7x}{3x + 2}\)**: The numerator is \( 7x \) and the denominator is \( 3x + 2 \). - **Exponent \(\ln 5\)**: The fraction is raised to the power of the natural logarithm of 5. This function combines elements of logarithms, roots, and exponents to showcase a more complex mathematical relationship.
Transcribed Image Text:**Equation 78:** \( y = \log_5 \sqrt{\left( \frac{7x}{3x + 2} \right)^{\ln 5}} \) **Explanation:** This mathematical expression defines the function \( y \) in terms of \( x \). Here's a breakdown: - **\( \log_5 \)**: This denotes a logarithm with base 5. - **Square Root**: The expression inside the square root is raised to a certain power, and then the square root is taken. - **Fraction \(\frac{7x}{3x + 2}\)**: The numerator is \( 7x \) and the denominator is \( 3x + 2 \). - **Exponent \(\ln 5\)**: The fraction is raised to the power of the natural logarithm of 5. This function combines elements of logarithms, roots, and exponents to showcase a more complex mathematical relationship.
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