Solution 1.2:1b

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We use the product rule with
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<center> [[Image:1_2_1b.gif]] </center>
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<math>x^{2}</math>
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and
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<math>\ln x</math>
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as factors:
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<math>\begin{align}
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& \left( x^{2}\ln x \right)^{\prime }=\left( x^{2} \right)^{\prime }\ln x+x^{2}\left( \ln x \right)^{\prime } \\
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& \\
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& =2x\centerdot \ln x+x^{2}\centerdot \frac{1}{x}=2x\ln x+x \\
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\end{align}</math>

Revision as of 14:38, 12 September 2008

We use the product rule with \displaystyle x^{2} and \displaystyle \ln x as factors:


\displaystyle \begin{align} & \left( x^{2}\ln x \right)^{\prime }=\left( x^{2} \right)^{\prime }\ln x+x^{2}\left( \ln x \right)^{\prime } \\ & \\ & =2x\centerdot \ln x+x^{2}\centerdot \frac{1}{x}=2x\ln x+x \\ \end{align}

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