Find `dy/dx` if :
`y=(x-1)^(-3),xne1`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = (x - 1)^{-3}\), we will use the power rule of differentiation. Here are the steps:

### Step-by-Step Solution:

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

2. **Apply the power rule**:
The power rule states that if \(y = u^n\), then \(\frac{dy}{dx} = n \cdot u^{n-1} \cdot \frac{du}{dx}\). In our case, \(u = (x - 1)\) and \(n = -3\).

3. **Differentiate the outer function**:
\[ \frac{dy}{du} = -3 \cdot (x - 1)^{-4} \]

4. **Differentiate the inner function**:
The derivative of \(u = (x - 1)\) with respect to \(x\) is:
\[ \frac{du}{dx} = 1 \]

5. **Combine the derivatives**:
Now, we apply the chain rule:
\[ \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = -3 \cdot (x - 1)^{-4} \cdot 1 \]

6. **Final result**:
Thus, we have:
\[ \frac{dy}{dx} = -\frac{3}{(x - 1)^4} \]

### Final Answer:
\[ \frac{dy}{dx} = -\frac{3}{(x - 1)^4} \]