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Question
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
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Solution
\[\frac{d}{dx}\left( \frac{\left( x + 5 \right)\left( 2 x^2 - 1 \right)}{x} \right)\]
\[ = \frac{d}{dx}\left( \frac{2 x^3 + 10 x^2 - x - 5}{x} \right)\]
\[ = \frac{d}{dx}\left( \frac{2 x^3}{x} \right) + \frac{d}{dx}\left( \frac{10 x^2}{x} \right) - \frac{d}{dx}\left( \frac{x}{x} \right) - \frac{d}{dx}\left( \frac{5}{x} \right)\]
\[ = 2\frac{d}{dx}\left( x^2 \right) + 10\frac{d}{dx}\left( x \right) - \frac{d}{dx}\left( 1 \right) - 5\frac{d}{dx}\left( x^{- 1} \right)\]
\[ = 2\left( 2x \right) + 10\left( 1 \right) - 0 - 5\left( - 1 \right) x^{- 2} \]
\[ = 4x + 10 + \frac{5}{x^2}\]
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