Differentiate the following functions with respect to x :

$\frac{(x + 5) (2 x^{2} - 1)}{x}$

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Solution

We have,

$\frac{d}{d x} {\frac{(x + 5) (2 x^{2} - 1)}{x}}$

$= \frac{d}{d x} (\frac{2 x^{3} + 10 x^{2} - x - 5}{x})$

$= \frac{d}{d x} (2 x^{2} + 10 x - 1 - 5 x^{- 1})$

$= 2 \frac{d}{d x} (x^{2}) + 10 \frac{d}{d x} (x) - \frac{d}{d x} (1) - 5 \frac{d}{d x} (x^{- 1})$

$= 2 \times 2 x + 10 - 0 + \frac{5}{x^{2}}$

$= 4 x + 10 + \frac{5}{x^{2}}$

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