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