Function Expression :
\[f(x)=\frac{-4}{e^x+1}-x+3 \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=-1 + \frac{4 e^{x}}{\left(e^{x} + 1\right)^{2}} \]\[f^{\,\prime}(x)=-1 + \frac{1}{\cosh^{2}{\left(\frac{x}{2} \right)}} \]
\[f^{\,\prime}(x)=\frac{1 - \cosh^{2}{\left(\frac{x}{2} \right)}}{\cosh^{2}{\left(\frac{x}{2} \right)}} \]
Integral
\[F(x) = - \frac{x^{2}}{2} - x + 4 \log{\left(e^{x} + 1 \right)} \]Sign Table
Variation Table
Plot
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