Find first derivative of y w.r.t. x.
(i) `y=e^(-x)` , (ii) `y=4 sin 3x` , (iii) `y=4e^(x^(2)-2x)`

Explanation

To find the first derivative of \( y \) with respect to \( x \) for the given functions, we will apply the rules of differentiation including the chain rule. Let's solve each part step by step.

### (i) \( y = e^{-x} \)

1. **Identify the function**: We have \( y = e^{-x} \).
2. **Differentiate using the chain rule**:
\[
\frac{dy}{dx} = \frac{d}{dx}(e^{-x}) = e^{-x} \cdot \frac{d}{dx}(-x)
...