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