Differentiate the following w.r.t. x:(i) `e^(-x)` (ii) `sin (log x), x > 0` (iii) `cos^(-1)(e^x)` (iv) `e^(cosx)`

Explanation

Let's differentiate each of the given functions step by step.

### (i) Differentiate \( e^{-x} \)

1. **Identify the function**: The function is \( e^{-x} \).
2. **Apply the chain rule**: The derivative of \( e^u \) with respect to \( x \) is \( e^u \cdot \frac{du}{dx} \).
- Here, \( u = -x \), so \( \frac{du}{dx} = -1 \).
3. **Differentiate**:
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