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