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Introduction

Find the deri...

Question

Find the derivative of
$x^{2} (3 - 6 x^{- 9})$

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Solution

$\frac{d}{d x} (x^{2} (3 - 6 x^{- 9}))$
$= \frac{d}{d x} (3 x^{2} - 6 x^{- 9 + 2})$
$= \frac{d}{d x} (3 x^{2} - 6 x^{- 7})$
$= \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (- 6 x^{- 7})$
$= 3 \frac{d}{d x} (x^{2}) - 6 \frac{d}{d x} (x^{- 7})$
$= 3 (2 x^{2 - 1}) + 42 (x^{- 7 - 1})$
$= 6 x + 42 x^{- 8}$
$= 6 x + \frac{42}{x^{8}}$

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