Find the derivative of `x^n+a x^(n-1)1+a^2x^(n-2)+dotdotdot+a^(n-1)x+a^n`for some fixed real number a.

Explanation

To find the derivative of the expression \( x^n + a x^{n-1} + a^2 x^{n-2} + \ldots + a^{n-1} x + a^n \), we can recognize that this is a polynomial in \( x \) with coefficients that are powers of \( a \).

### Step-by-Step Solution:

1. **Identify the expression**:
The expression can be written as:
\[
f(x) = x^n + a x^{n-1} + a^2 x^{n-2} + \ldots + a^{n-1} x + a^n
...