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

Explanation

To evaluate the derivative of \( \frac{1}{x} \) with respect to \( x \), we can follow these steps:

### Step 1: Rewrite the function
The function \( \frac{1}{x} \) can be rewritten using negative exponents:
\[ \frac{1}{x} = x^{-1} \]

### Step 2: Apply the power rule of differentiation
Now, we will differentiate \( x^{-1} \) using the power rule. The power rule states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \). Here, \( n = -1 \):
\[ \frac{d}{dx}(x^{-1}) = -1 \cdot x^{-1 - 1} = -1 \cdot x^{-2} \]

### Step 3: Simplify the expression
Now, we simplify the expression we obtained:
\[ -1 \cdot x^{-2} = -\frac{1}{x^2} \]

### Final Result
Thus, the derivative of \( \frac{1}{x} \) with respect to \( x \) is:
\[ \frac{d}{dx}\left(\frac{1}{x}\right) = -\frac{1}{x^2} \]

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