The differentiation of `t a nx` with respect to x is `sec^2xdot` i.e. `d/(dx)(tanx)=sec^2x`

Explanation

To differentiate the function \( \tan x \) with respect to \( x \) and prove that \( \frac{d}{dx}(\tan x) = \sec^2 x \), we will use the first principle of derivatives.

### Step-by-Step Solution:

1. **Define the Function**:
Let \( f(x) = \tan x \).

2. **Apply the First Principle of Derivatives**:
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