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Question
x5 ex + x6 log x
Solution
\[ = x^5 \frac{d}{dx}\left( e^x \right) + e^x \frac{d}{dx}\left( x^5 \right) + x^6 \frac{d}{dx}\left( \log x \right) + \log x \frac{d}{dx}\left( x^6 \right)\]
\[ = x^5 e^x + e^x \left( 5 x^4 \right) + x^6 . \frac{1}{x} + \log x\left( 6 x^5 \right)\]
\[ = x^5 e^x + e^x \left( 5 x^4 \right) + x^5 + \log x\left( 6 x^5 \right)\]
\[ = x^4 \left( x e^x + 5 e^x + x + 6x \log x \right)\]
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