Function Expression :
\[f(x)=\frac{x}{3^x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 3^{- x} x \log{\left(3 \right)} + \frac{1}{3^{x}} \]\[f^{\,\prime}(x)=3^{- x} \left(- x \log{\left(3 \right)} + 1\right) \]
\[ \]
Integral
\[F(x) = \frac{3^{- x} \left(- x \log{\left(3 \right)} - 1\right)}{\log{\left(3 \right)}^{2}} \]Sign Table
Variation Table
Plot
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