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a) y = (3x²-7) 5 (x²+x)9 7x b) x= c²² Sin²x (x²_qx+5)³ C) y = (Sinx) Sin - ² x 3

a) y = (3x²-7) 5 (x²+x)9 7x b) x= c²² Sin²x (x²_qx+5)³ C) y = (Sinx) Sin - ² x 3

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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use logarithm to find y' for the expressions. thank you. 

Below are the mathematical expressions provided for educational purposes: a) \( y = (3x^2 - 7)^5 (x^4 + x)^9 \) This expression is a product of two polynomial functions, each raised to a power. The first polynomial is \( 3x^2 - 7 \) raised to the 5th power, and the second polynomial is \( x^4 + x \) raised to the 9th power. b) \( y = \frac{e^{7x} \sin^2 y}{(x^2 - 9x + 5)^3} \) This is a more complex expression involving an exponential function \( e^{7x} \), the square of the sine function \( \sin^2 y \), and a polynomial in the denominator \( (x^2 - 9x + 5) \) raised to the 3rd power. c) \( y = (\sin x)^{\sin^{-1} x} \) In this expression, the sine function \( \sin x \) is raised to the power of its inverse function \( \sin^{-1} x \) (also known as the arcsine). Each of these expressions showcases different mathematical functions and operations, including powers, trigonometric functions, exponential functions, and polynomial expressions. Understanding how to work with such expressions is fundamental in higher mathematics.
Transcribed Image Text:Below are the mathematical expressions provided for educational purposes: a) \( y = (3x^2 - 7)^5 (x^4 + x)^9 \) This expression is a product of two polynomial functions, each raised to a power. The first polynomial is \( 3x^2 - 7 \) raised to the 5th power, and the second polynomial is \( x^4 + x \) raised to the 9th power. b) \( y = \frac{e^{7x} \sin^2 y}{(x^2 - 9x + 5)^3} \) This is a more complex expression involving an exponential function \( e^{7x} \), the square of the sine function \( \sin^2 y \), and a polynomial in the denominator \( (x^2 - 9x + 5) \) raised to the 3rd power. c) \( y = (\sin x)^{\sin^{-1} x} \) In this expression, the sine function \( \sin x \) is raised to the power of its inverse function \( \sin^{-1} x \) (also known as the arcsine). Each of these expressions showcases different mathematical functions and operations, including powers, trigonometric functions, exponential functions, and polynomial expressions. Understanding how to work with such expressions is fundamental in higher mathematics.
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