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