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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.6 - Problem 24e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.6 - Problem 24e

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# Without evaluating derivatives which of the following

ISBN: 9780321570567 2

## Solution for problem 24E Chapter 4.6

Calculus: Early Transcendentals | 1st Edition

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Problem 24E

Without evaluating derivatives which of the following functions have the same 2 2 derivative: f(x) = ln x, g(x) = ln 2x, h(x) = ln x , p(x) = ln 10x ? ?

Step-by-Step Solution:

Solution 24E Step 1 In this problem we have to find which of the given functions have same derivative by using the fact that “Two differentiable functions, that differ by a constant always have the same derivative” … (1) First let us consider f(x)and g(x) Given f(x) = ln x, g(x) = ln 2x f(x)g(x) = ln x ln 2x By using ln (mn) = ln m + ln nto ln 2xwe get, = ln x (ln 2+ln x) = ln x ln 2 ln x = ln 2 f(x)g(x) = ln 2where ln 2is a constant. Therefore by ( 1) we get, f(x)and g(x)have same derivative.

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