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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 6.7 - Problem 7e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 6.7 - Problem 7e

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# Answer: Derivatives with ln x Evaluate the following

ISBN: 9780321570567 2

## Solution for problem 7E Chapter 6.7

Calculus: Early Transcendentals | 1st Edition

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Problem 7E

Problem 7E

Derivatives with ln x Evaluate the following derivatives.

Step-by-Step Solution:
Step 1 of 3

Solution 7E Step-1 Logarithmic function ; Let , f( x) = ln(x). we know that ln(x) is not defined for all negative values of x , and zero.So , if x0 , then ln(x) is not defined.that means the function is defined only positive values of x . That is , if x > 0 , then f(x) = ln(x) is defined. Therefore , the domain of the function f(x) = ln(x) is (0 , ). To finding the range of the function f(x) = ln(x) draw the graph of the function. The graph of f(x) = ln(x) is Clearly from the graph the domain of f(x) = ln(x) is (0,) , and from observing the curve , we can see the range is between - and . We could write this as - y . Therefore , the range of f(x) is (-, ). Step-2 Now , we have to evaluate d (x ln(x ))| x = 1. dx 3 Let f(x) = x ln(x )..............(1) f(x) = x (3ln(x)) , since ln(a ) = x ln(a) Differentiate both sides with respect to x , then we have d f(x) = d (x (3ln(x)) dx dx dx f(x) = x dx (3 ln(x)) + (3ln(x) dx(x) , since dx (uv) = u dx (v) +v dx (u). 1 d 1 d d d = x (3( )x + 3 ln(x) (1) , since dxln(x) = x( dx(x)) , dx Cx = C dx (x), C is constant. = 3 + 3 ln(x) ………………(2) From (1) , (2) d dx(x ln(x )) = 3( 1+ln(x))................(3) Step-3 Now , we have to find the value of d (x ln(x ))| . dx x = 1 d From (3 ) , dx (x ln(x )) = 3( 1+ln(x)) d (x ln(x ))| = (3(1+ln(x))| . dx x = 1 x = 1 = 3 (1+ln(1)) , since x =1. = 3(1+0) , since ln(1) = 0. = 3. d 3 Therefore , dx ( ln(x ))| x = 1 = 3.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

This full solution covers the following key subjects: Derivatives, valuate. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Derivatives with ln x Evaluate the following derivatives.” is broken down into a number of easy to follow steps, and 8 words. The full step-by-step solution to problem: 7E from chapter: 6.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 7E from 6.7 chapter was answered, more than 376 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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