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