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Question
x2 ex log x
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Solution
\[\text{ Let } u = x^2 ; v = e^x ; w = \log x\]
\[\text{ Then }, u' = 2x; v' = e^x , w = \frac{1}{x}\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uvw \right) = u'vw + + uv'w + uvw'\]
\[\frac{d}{dx}\left( x^2 e^x \log x \right) = 2x e^x \log x + x^2 e^x \log x + x^2 e^x \frac{1}{x}\]
\[ = 2x e^x \log x + x^2 e^x \log x + x e^x \]
\[ = x e^x \left( 2 \log x + x \log x + 1 \right)\]
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