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Question
(1 +x2) cos x
Solution
\[Then , u' = 2x; v' = - \sin x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ \left( 1 + x^2 \right)\left( \cos x \right) \right] = \left( 1 + x^2 \right)\left( - \sin x \right) + \left( \cos x \right)\left( 2x \right)\]
\[ = - \sin x - x^2 \sin x + 2x \cos x\]
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