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?

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