Function Expression :
\[f(x)=1-\frac{x}{e^{-x}+1} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{x e^{- x}}{\left(1 + e^{- x}\right)^{2}} - \frac{1}{1 + e^{- x}} \]\[f^{\,\prime}(x)=- \frac{x + e^{x} + 1}{4 \cosh^{2}{\left(\frac{x}{2} \right)}} \]
\[ \]
Integral
\[F(x) = - \int \left(- \frac{e^{x}}{e^{x} + 1}\right)\, dx - \int \frac{x e^{x}}{e^{x} + 1}\, dx - \int \left(- \frac{1}{e^{x} + 1}\right)\, dx \]Sign Table
Variation Table
Plot
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