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