Function Expression :
\[f(x)=\frac{1}{e^x+e^{-x}} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{- e^{x} + e^{- x}}{\left(e^{x} + e^{- x}\right)^{2}} \]\[f^{\,\prime}(x)=\frac{\left(1 - e^{2 x}\right) e^{x}}{\left(e^{2 x} + 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + e^{x} \right)} \right)\right)} \]Sign Table
Variation Table
Plot
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