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