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