Find derivative of `sin(tan^(-1)e^(-x))` w.r.t. to `x`

Explanation

To find the derivative of the function \( y = \sin(\tan^{-1}(e^{-x})) \) with respect to \( x \), we will use the chain rule of differentiation.

### Step-by-Step Solution:

1. **Identify the outer and inner functions**:
- The outer function is \( \sin(u) \) where \( u = \tan^{-1}(e^{-x}) \).
- The inner function is \( u = \tan^{-1}(v) \) where \( v = e^{-x} \).

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