Find the derivative of the following functions from the first principle
(i) `x^(3) + 4x^(2)` (ii) `sqrt(x + 1)`

Explanation

To find the derivative of the given functions using the first principle of derivatives, we will follow a systematic approach.

### Part (i): Derivative of \( f(x) = x^3 + 4x^2 \)

1. **Define the function**:
\[ f(x) = x^3 + 4x^2 \]
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