Please answer d and e and show steps 1. Find the derivative of each function.(a) $ f(\theta) = \ln(\sin \theta) + \sin(\ln \theta) $.(b) $ f(x) = \log_{10}(1 + \cos x) $.(c) $ y = \ln |x^3 - x^2| $.(d) $ G(x) = \ln \left( \frac{a-x}{a+x} \right) $.(e) $ y = x^2 \ln[\ln x] $.

Answered: D a + x a-x u = (x) (p)

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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Please answer d and e and show steps

1. Find the derivative of each function.

(a) $ f(\theta) = \ln(\sin \theta) + \sin(\ln \theta) $.

(b) $ f(x) = \log_{10}(1 + \cos x) $.

(c) $ y = \ln |x^3 - x^2| $.

(d) $ G(x) = \ln \left( \frac{a-x}{a+x} \right) $.

(e) $ y = x^2 \ln[\ln x] $.

Expert Solution

Step 1: To find derivative

since you have posted multiple question in this question which are not interlinked so i have solved first question as per our company guidelines kindly post other question in the next question.

(d)

$G left parenthesis x right parenthesis equals ln open parentheses fraction numerator a minus x over denominator a plus x end fraction close parentheses$