`y=tan^(-1)(secx+tanx)`. Then `(dy)/(dx)=`

Explanation

To find the derivative of the function \( y = \tan^{-1}(\sec x + \tan x) \), we will follow these steps:

### Step 1: Differentiate the function
We start by applying the chain rule for differentiation. The derivative of \( \tan^{-1}(u) \) is given by \( \frac{1}{1 + u^2} \cdot \frac{du}{dx} \), where \( u = \sec x + \tan x \).

### Step 2: Find \( \frac{du}{dx} \)
We need to differentiate \( u = \sec x + \tan x \):
- The derivative of \( \sec x \) is \( \sec x \tan x \).
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