Find the derivative of x^ -4 (3-4 x^ -5 ) - Vidyadip

Question

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

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Answer

Here $f(x)=x^{-4}\left(3-4 x^{-5}\right)$
$f^{\prime}(x)=\frac{d}{d x}\left[x^{-4}\left(3-4 x^{-5}\right)\right]$
$=x^{-4} \frac{d}{d x}\left(3-4 x^{-5}\right)+\left(3-4 x^{-5}\right) \frac{d}{d x}\left(x^{-4}\right)$
$=x^{-4}\left(20 x^{-6}\right)+\left(3-4 x^{-5}\right)\left(-4 x^{-5}\right)$
$=20 x^{-10}-12 x^{-5}+16 x^{-10}$
$=36 x^{-10}-12 x^{-5}$
$=\frac{36}{x^{10}}$
$=\frac{12}{x^5}$

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