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