Differentiate each function by applying the basic rules of differentiation
`(9x^(8)-8x^(9))(x+(1)/(x))`

Explanation

To differentiate the function \( (9x^{8} - 8x^{9})(x + \frac{1}{x}) \), we will apply the product rule of differentiation. The product rule states that if you have two functions \( u(x) \) and \( v(x) \), then the derivative of their product is given by:

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

### Step-by-Step Solution:

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