Differentiate the function f(x) = sec `(tan sqrt(x)))` with respect to x,

Explanation

To differentiate the function \( f(x) = \sec(\tan(\sqrt{x})) \) with respect to \( x \), we will use the chain rule. Here’s a step-by-step solution:

### Step 1: Identify the outer and inner functions
The function can be broken down as follows:
- Outer function: \( \sec(u) \) where \( u = \tan(\sqrt{x}) \)
- Inner function 1: \( u = \tan(v) \) where \( v = \sqrt{x} \)
- Inner function 2: \( v = \sqrt{x} \)

...