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