Find the derivative of x^5 (3-6 x^ -9 ) - Vidyadip

Question

Find the derivative of $x^5\left(3-6 x^{-9}\right)$

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Answer

$\text { Here } f(x)=x^5\left(3-6 x^{-9}\right)$
$=x^5 \frac{d}{d x}\left(3-6 x^{-9}\right)+\left(3-6 x^{-9}\right) \frac{d}{d x}\left(x^5\right)$
$=x^5\left(54 x^{-10}\right)+\left(3-6 x^{-9}\right) \times 5 x^4$
$=54 x^{-5}+15 x^4-30 x^{-5}$
$=24 x^{-5}+15 x^4$
$=\frac{24}{x^5}+15 x^4$

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