Find the derivative of $x^{- 3} (5 + 3 x)$

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Solution

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

$= \frac{d}{d x} (5 x^{- 3} + 3 x^{1 - 3})$

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

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

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

$= 5 (- 3 x^{- 3 - 1}) + 3 (- 2 x^{- 2 - 1})$

$= - 15 x^{- 4} - 6 x^{- 3}$

$= \frac{15}{x^{4}} - \frac{6}{x^{3}}$

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