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Question
x3 sin x
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Solution
\[\text{ Let } u = x^3 ; v = \sin x\]
\[\text{ Then }, u' = 3 x^2 ; v' = \cos x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^3 \sin x \right) = x^3 \cos x + \sin x \left( 3 x^2 \right)\]
\[ = x^2 \left( x \cos x + 3 \sin x \right)\]
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