Differentiate the following functions with respect to x :

$\frac{2 x^{2} + 3 x + 4}{x}$

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Solution

We have,

$\frac{d}{d x} (\frac{2 x^{2} + 3 x + 4}{x})$

$= \frac{d}{d x} (\frac{2 x^{2}}{x} + \frac{3 x}{x} + \frac{4}{x}) = \frac{d}{d x} (2 x + 3 + 4 x^{- 1}) = 2 - \frac{4}{x^{2}}$

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