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