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 of differentiation, which states that if \( u \) and \( v \) are functions of \( x \), then the derivative of their product is given by:

\[ \frac{d}{dx}(uv) = u'v + uv' \]

We will also use the chain rule and the derivatives of standard functions where necessary.

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