`d/(dx) (Ax + B)^(n)`

Explanation

To differentiate the function \( y = (Ax + B)^n \) with respect to \( x \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Function**:
We start with the function:
\[ y = (Ax + B)^n \]

2. **Substitute for Simplicity**:
Let \( t = Ax + B \). This simplifies our function to:
\[ y = t^n \]

3. **Differentiate Using Chain Rule**:
According to the chain rule, the derivative of \( y \) with respect to \( x \) can be expressed as:
\[ \frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx} \]

4. **Differentiate \( y \) with respect to \( t \)**:
Now, we differentiate \( y = t^n \) with respect to \( t \):
\[ \frac{dy}{dt} = n \cdot t^{n-1} \]

5. **Differentiate \( t \) with respect to \( x \)**:
Next, we differentiate \( t = Ax + B \) with respect to \( x \):
\[ \frac{dt}{dx} = A \]

6. **Combine the Results**:
Now, substituting back into the chain rule expression:
\[ \frac{dy}{dx} = n \cdot t^{n-1} \cdot A \]

7. **Substitute \( t \) Back**:
Finally, we substitute \( t \) back in terms of \( x \):
\[ \frac{dy}{dx} = n \cdot A \cdot (Ax + B)^{n-1} \]

### Final Answer:
Thus, the derivative of \( (Ax + B)^n \) with respect to \( x \) is:
\[ \frac{d}{dx} (Ax + B)^n = nA (Ax + B)^{n-1} \]