Differentiate the following with respect to `x :` (i) `x^3e^xsinx` (ii) `xsinxlogx` (iii) `x^n(log)_a xe^x`

Explanation

To differentiate the given functions with respect to \( x \), we will use the product rule and chain rule of differentiation. Let's solve each part step by step.

### Part (i): Differentiate \( y = x^3 e^x \sin x \)

1. **Identify the functions**:
Let \( u = x^3 \), \( v = e^x \), and \( w = \sin x \).

2. **Apply the product rule**:
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