Function Expression :
\[f(x)=\frac{(e^x-1 )}{2e^x+1} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -1 \]\[\lim_{x \rightarrow+\infty}f(x) = \frac{1}{2} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 \left(e^{x} - 1\right) e^{x}}{\left(2 e^{x} + 1\right)^{2}} + \frac{e^{x}}{2 e^{x} + 1} \]\[f^{\,\prime}(x)=\frac{3 e^{x}}{\left(2 e^{x} + 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = - x + \frac{3 \log{\left(e^{x} + \frac{1}{2} \right)}}{2} \]Sign Table
Variation Table
Plot
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