Function Expression :
\[f(x)=2ln(x )-(ln x )^2 \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 \log{\left(x \right)}}{x} + \frac{2}{x} \]\[f^{\,\prime}(x)=\frac{2 \cdot \left(1 - \log{\left(x \right)}\right)}{x} \]
\[ \]
Integral
\[F(x) = - x \log{\left(x \right)}^{2} + 4 x \log{\left(x \right)} - 4 x \]Sign Table
Variation Table
Plot
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