Differentiate `sqrt(x^2+x+1)` with respect to `x` :

Explanation

To differentiate the function \( f(x) = \sqrt{x^2 + x + 1} \) with respect to \( x \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the function**:
Let \( u = x^2 + x + 1 \). Therefore, we can rewrite the function as:
\[
f(x) = \sqrt{u} = u^{1/2}
...