Find the derivative of
$x^{- 4} (3 - 4 x^{- 5})$

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Solution

$x^{- 4} (3 - 4 x^{- 5})$
$= 3 x^{- 4} - 4 x^{- 5 - 4}$
$= 3 x^{- 4} - 4 x^{- 9}$
Differential of $x^{- 4} (3 - 4 x^{- 5}) =$ Differential of $= 3 x^{- 4} - 4 x^{- 9}$
$= \frac{d}{d x} (3 x^{- 4} - 4 x^{- 9})$
$= \frac{d}{d x} (3 x^{- 4}) - \frac{d}{d x} (4 x^{- 9})$
$= 3 \frac{d}{d x} (x^{- 4}) - 4 \frac{d}{d x} (x^{- 9})$
$= 4 (- 4 x^{- 4 - 1}) - 4 (- 9 x^{- 9 - 1})$
$= - 16 x^{- 5} + 36 x^{- 10}$

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