Find the derivative of the following functions using first principle of derivative.
(i)`tan(x + 1)`
(ii) `cot (x^(2) + 1)`

Explanation

To find the derivative of the functions \( f(x) = \tan(x + 1) \) and \( g(x) = \cot(x^2 + 1) \) using the first principle of derivatives, we will follow these steps:

### Part (i): Derivative of \( f(x) = \tan(x + 1) \)

1. **Apply the First Principle of Derivative**:
\[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} \]
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