Differentiate `x^(6)` from the first principle.

Explanation

To differentiate \( y = x^6 \) from the first principle, we will follow these steps:

### Step 1: Define the function and increment
Let \( y = x^6 \). We will consider an increment in \( x \), denoted as \( \Delta x \). Therefore, the new value of \( x \) becomes \( x + \Delta x \).

### Step 2: Calculate the increment in \( y \)
The increment in \( y \), denoted as \( \Delta y \), can be expressed as:
\[
...