Find the derivative of the function given by `f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)`and hence find `f^(prime)(1)`.

Explanation

To find the derivative of the function \( f(x) = (1+x)(1+x^2)(1+x^4)(1+x^8) \) and then evaluate \( f'(1) \), we can follow these steps:

### Step 1: Expand the function
We will first expand the function \( f(x) \).

1. **Multiply \( (1+x) \) and \( (1+x^2) \)**:
\[
(1+x)(1+x^2) = 1 + x + x^2 + x^3
...