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

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