Differentiate the following function with respect to x.
$x^{5} (3 - 6 x^{- 9})$ .

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Solution

Given expression

$x^{5} (3 - 6 x^{- 9})$

$= 3 x^{5} - 6 x^{- 4}$

differentiating w.r.t. $x$ , we get

$\frac{d}{d x} (3 x^{5} - 6 x^{- 4})$

$\frac{d}{d x} (3 x^{5}) - \frac{d}{d x} 6 x^{- 4}$

$⟹ 15 x^{4} + 24 x^{- 5}$

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