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Question
x5 (3 − 6x−9)
Solution
\[\text{ Let } u = x^5 ; v = \left( 3 - 6 x^{- 9} \right)\]
\[\text{ Then }, u' = 5 x^4 ; v' = 54 x^{- 10} \]
\[\text{ Using theproduct rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ x^5 \left( 3 - 6 x^{- 9} \right) \right] = x^5 \left( 54 x^{- 10} \right) + \left( 3 - 6 x^{- 9} \right)\left( 5 x^4 \right)\]
\[ = 54 x^{- 5} + 15 x^4 - 30 x^{- 5} \]
\[ = 15 x^4 + 24 x^{- 5}\]
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