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Differentiate the following: a) y = ln(5x) (b) y = In In(³) (c) y = In(x³)

Differentiate the following: a) y = ln(5x) (b) y = In In(³) (c) y = In(x³)

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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**Differentiate the following:** (a) \( y = \ln(5x) \) (b) \( y = \ln\left(\frac{5}{x}\right) \) (c) \( y = \ln(x^3) \) (d) \( y = (\ln x)^3 \) (e) \( y = x \sqrt{\ln x} \) (f) \( y = \frac{\ln x}{x} \) (g) \( y = \ln(\sec(\ln \theta)) \) (h) \( y = \ln(\sec \theta + \tan \theta) \) (i) \( y = \frac{(x^2 - 3)\sqrt{x^2 + 1}}{(x+5)^{2/3} \cos^x} \) (j) \( y = (\ln x)^{\cos x} \) (k) \( y = (\cos x)^{\ln x} \)
Transcribed Image Text:**Differentiate the following:** (a) \( y = \ln(5x) \) (b) \( y = \ln\left(\frac{5}{x}\right) \) (c) \( y = \ln(x^3) \) (d) \( y = (\ln x)^3 \) (e) \( y = x \sqrt{\ln x} \) (f) \( y = \frac{\ln x}{x} \) (g) \( y = \ln(\sec(\ln \theta)) \) (h) \( y = \ln(\sec \theta + \tan \theta) \) (i) \( y = \frac{(x^2 - 3)\sqrt{x^2 + 1}}{(x+5)^{2/3} \cos^x} \) (j) \( y = (\ln x)^{\cos x} \) (k) \( y = (\cos x)^{\ln x} \)
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a right parenthesis thin space y equals ln open parentheses 5 x close parentheses b right parenthesis space y equals ln open parentheses 5 over x close parentheses c right parenthesis space y equals ln open parentheses x cubed close parentheses

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