Evaluate:
`(d)/(dx)((1)/(x^(3)))`

Explanation

To evaluate the derivative of the function \( \frac{1}{x^3} \) with respect to \( x \), we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Function:**
The function \( \frac{1}{x^3} \) can be rewritten using negative exponents:
\[ \frac{1}{x^3} = x^{-3} \]

2. **Apply the Power Rule:**
We will use the power rule of differentiation, which states that if \( f(x) = x^n \), then \( \frac{d}{dx}(x^n) = n \cdot x^{n-1} \). Here, \( n = -3 \):
\[ \frac{d}{dx}(x^{-3}) = -3 \cdot x^{-3-1} = -3 \cdot x^{-4} \]

3. **Simplify the Expression:**
The expression \( -3 \cdot x^{-4} \) can be rewritten back in terms of positive exponents:
\[ -3 \cdot x^{-4} = -\frac{3}{x^4} \]

4. **Final Result:**
Therefore, the derivative of \( \frac{1}{x^3} \) with respect to \( x \) is:
\[ \frac{d}{dx}\left(\frac{1}{x^3}\right) = -\frac{3}{x^4} \]

### Summary:
The derivative of \( \frac{1}{x^3} \) is \( -\frac{3}{x^4} \).