Find the derivative of the following functions.
(i) `(x^(2) tan x)` (ii) `(x + cos x) (sqrt(x) + 1)` (iii) `x^(-3) (e^(x) + 5 "sin" x)`

Explanation

To find the derivatives of the given functions, we will apply the product rule and the chain rule of differentiation. Let's solve each part step by step.

### (i) Derivative of \( y = x^2 \tan x \)

1. **Identify the functions**: Let \( u = x^2 \) and \( v = \tan x \).
2. **Apply the product rule**: The product rule states that if \( y = u \cdot v \), then \( \frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx} \).
3. **Differentiate \( u \) and \( v \)**:
- \( \frac{du}{dx} = 2x \)
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