Obtian `(dy)/(dx)` for the following :
`y=x^(-3)`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = x^{-3}\), we will use the power rule of differentiation. The power rule states that if \(y = x^n\), then \(\frac{dy}{dx} = n \cdot x^{n-1}\).

### Step-by-step Solution:

1. **Identify the function**:
We have \(y = x^{-3}\).

2. **Apply the power rule**:
According to the power rule, if \(y = x^n\), then:
\[ \frac{dy}{dx} = n \cdot x^{n-1} \]
Here, \(n = -3\).

3. **Differentiate**:
Substitute \(n = -3\) into the power rule:
\[ \frac{dy}{dx} = -3 \cdot x^{-3-1} \]

4. **Simplify the expression**:
Now simplify the exponent:
\[ \frac{dy}{dx} = -3 \cdot x^{-4} \]

5. **Final result**:
Thus, the derivative \(\frac{dy}{dx}\) is:
\[ \frac{dy}{dx} = -\frac{3}{x^4} \]

### Summary:
The derivative of \(y = x^{-3}\) is \(\frac{dy}{dx} = -\frac{3}{x^4}\).