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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find the derivitive of each function please
![This page presents a series of mathematical functions for educational purposes:
(a) The function \( f(\theta) = \ln(\sin \theta) + \sin(\ln \theta) \). This function combines the natural logarithm and sine functions with the variable \(\theta\).
(b) The function \( f(x) = \log_{10}(1 + \cos x) \). Here, the logarithm to base 10 is applied to the expression \(1 + \cos x\).
(c) The function \( y = \ln |x^3 - x^2| \). This involves the natural logarithm of the absolute value of the expression \(x^3 - x^2\).
(d) The function \( G(x) = \ln \left(\frac{a - x}{a + x}\right) \). It takes the natural logarithm of the fraction \(\frac{a - x}{a + x}\), where \(a\) is a constant.
(e) The function \( y = x^2 \ln[\ln x] \). This involves multiplying \(x^2\) by the natural logarithm of the natural logarithm of \(x\).
These functions illustrate the use of logarithmic and trigonometric operations in mathematical expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44d0f866-3879-4a95-bacc-717e14c65c8b%2Fcc406235-d3b3-4a99-9300-0e5d64efcf96%2F08a0ind_processed.png&w=3840&q=75)
Transcribed Image Text:This page presents a series of mathematical functions for educational purposes:
(a) The function \( f(\theta) = \ln(\sin \theta) + \sin(\ln \theta) \). This function combines the natural logarithm and sine functions with the variable \(\theta\).
(b) The function \( f(x) = \log_{10}(1 + \cos x) \). Here, the logarithm to base 10 is applied to the expression \(1 + \cos x\).
(c) The function \( y = \ln |x^3 - x^2| \). This involves the natural logarithm of the absolute value of the expression \(x^3 - x^2\).
(d) The function \( G(x) = \ln \left(\frac{a - x}{a + x}\right) \). It takes the natural logarithm of the fraction \(\frac{a - x}{a + x}\), where \(a\) is a constant.
(e) The function \( y = x^2 \ln[\ln x] \). This involves multiplying \(x^2\) by the natural logarithm of the natural logarithm of \(x\).
These functions illustrate the use of logarithmic and trigonometric operations in mathematical expressions.
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