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Solved: How can you write any real power of x as a power

University Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321717399 | Authors: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr. ISBN: 9780321717399 65

Solution for problem 27E Chapter 3.R

University Calculus: Early Transcendentals | 2nd Edition

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University Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321717399 | Authors: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr.

University Calculus: Early Transcendentals | 2nd Edition

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Problem 27E

How can you write any real power of x as a power of e? Are there any restrictions on x? How does this lead to the Power Rule for differentiating arbitrary real powers?

Step-by-Step Solution:

Solution:-

Step 1 of 3</p>

Given that

We have to explain how can we write any real power of  as a power of e? Are there any restrictions on x? How does this lead to the Power Rule for differentiating arbitrary real powers?

Step 2 of 3</p>

We have to take any real power of  say

Suppose

This can be written as power of  as

        =

Therefore, we can write any real power of  as a power of e as .

 Yes,there are  restrictions on

Here, restriction on  is

Step 3 of 3

Chapter 3.R, Problem 27E is Solved
Textbook: University Calculus: Early Transcendentals
Edition: 2
Author: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr.
ISBN: 9780321717399

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