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

Question

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

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Answer

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

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