Evaluate:
`(d)/(dx)(x^(1//5))`

Explanation

To evaluate the derivative of the function \( f(x) = x^{1/5} \), we will use the power rule of differentiation. The power rule states that if \( f(x) = x^n \), then the derivative \( f'(x) \) is given by:

\[ f'(x) = n \cdot x^{n-1} \]

**Step 1: Identify the exponent.**

In our case, the exponent \( n \) is \( \frac{1}{5} \).

**Step 2: Apply the power rule.**

Using the power rule, we differentiate \( f(x) = x^{1/5} \):

\[ \frac{d}{dx}(x^{1/5}) = \frac{1}{5} \cdot x^{(1/5) - 1} \]

**Step 3: Simplify the exponent.**

Now, we simplify the exponent:

\[ (1/5) - 1 = \frac{1}{5} - \frac{5}{5} = -\frac{4}{5} \]

So we have:

\[ \frac{d}{dx}(x^{1/5}) = \frac{1}{5} \cdot x^{-4/5} \]

**Step 4: Rewrite in a more standard form.**

We can express \( x^{-4/5} \) as \( \frac{1}{x^{4/5}} \):

\[ \frac{d}{dx}(x^{1/5}) = \frac{1}{5} \cdot \frac{1}{x^{4/5}} = \frac{1}{5x^{4/5}} \]

Thus, the final result of the differentiation is:

\[ \frac{d}{dx}(x^{1/5}) = \frac{1}{5x^{4/5}} \]

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