Function Expression :
\[f(x)=-\frac{2}{xe^x} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 \left(- x e^{x} - e^{x}\right) e^{- 2 x}}{x^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(x + 1\right) e^{- x}}{x^{2}} \]
\[ \]
Integral
\[F(x) = - 2 \operatorname{Ei}{\left(x e^{i \pi} \right)} \]Sign Table
Variation Table
Plot
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