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

Explanation

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

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

### Step 1: Identify the functions
Let:
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