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 outer function is \( \sec(u) \) where \( u = \tan(\sqrt{x}) \). The inner function \( u \) itself is \( \tan(v) \) where \( v = \sqrt{x} \).

### Step 2: Differentiate the outer function
The derivative of \( \sec(u) \) with respect to \( u \) is:
\[
...