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Question
x−4 (3 − 4x−5)
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Solution
\[\text{ Let } u = x^{- 4} ; v = 3 - 4 x^{- 5} \]
\[\text{ Then }, u' = - 4 x^{- 5} ; v' = 20 x^{- 6} \]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ x^{- 4} \left( 3 - 4 x^{- 5} \right) \right] = x^{- 4} \left( 20 x^{- 6} \right) + \left( 3 - 4 x^{- 5} \right)\left( - 4 x^{- 5} \right)\]
\[ = 20 x^{- 10} - 12 x^{- 5} + 16 x^{- 10} \]
\[ = - 12 x^{- 5} + 36 x^{- 10}\]
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