Function Expression :
\[f(x)=xe^{-5x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 5 x e^{- 5 x} + e^{\left(-1\right) 5 x} \]\[f^{\,\prime}(x)=\left(1 - 5 x\right) e^{- 5 x} \]
\[ \]
Integral
\[F(x) = \frac{\left(- 5 x - 1\right) e^{- 5 x}}{25} \]Sign Table
Variation Table
Plot
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